National Socialism is a specific thing. You can't just take parts of the name and then assume what it means based on these parts (another example: The Democratic People's Republic of Korea is not a democracy). National Socialism is not simply a nationalist version of socialism (Stalin's Socialism in one country would be closer to that).

National Socialism is the ideology that Nazi Germany had. It is inherently antisemitic, racist, nationalist, völkisch, social-Darwinist, anti-communist, anti-liberal, and antidemocratic. Nazism cannot be separated from these ideas.

National Socialism did not want to change the relations of production (as socialists would), and expressions that might hint towards socialism were only catchphrases used for propaganda purposes.

Some try to temporarily separate Nazism from some of these concepts in an attempt to whitewash it and make it palatable to the mainstream. This is not possible. If you consider antisemitism, racism, or genocide to be "bad", then you should also consider National Socialists and those trying to defend them to be "bad".

Q: How does Hitler's interpretation of “Nationalist Socialism” relate to the modern interpretation of “Socialism” and “Nationalism”?

Short answer: The definitions of the words did not change that significantly in academic discourse. The "relations" between them have therefore also not changed.

The person of interest did not interpret any "Nationalist Socialism", but invented National-socialism. This National-Socialism was never any form of Socialism, not in theory, not in practice. National-socialism has a good deal of nationalism in its core beliefs and a genuine hatred for any form of socialism. For him "nationalism" was natural, socialism "unnatural".

This needs to be dissected for historical and current meanings or definitions.

Definitions, simple

Modern: socialism

noun [ U ] UK ​ /ˈsəʊ.ʃəl.ɪ.zəm/ US ​ /ˈsoʊ.ʃəl.ɪ.zəm/
​
C2 the set of beliefs that states that all people are equal and should share equally in a country's money, or the political systems based on these beliefs (the belief or theory that a country’s wealth (its land, mines, industries, railways etc) should belong to the people as a whole, not to private owners.)

Modern: national-socialism

National Socialism

noun [ U ] UK ​ /ˌnæʃ.ən.əl ˈsəʊ.ʃəl.ɪ.zəm/ US ​ /ˌnæʃ.ən.əl ˈsoʊ.ʃəl.ɪ.zəm/
​
→ Nazism: the beliefs and policies of the National Socialist (German Workers') Party, led by Adolf Hitler, which controlled Germany from 1933 to 1945.

Nazi
noun [ C ] UK ​ /ˈnɑːt.si/ US ​ /ˈnɑːt.si/
​
a member of the National Socialist (German Workers') Party, led by Adolf Hitler, which controlled Germany from 1933 to 1945
​
disapproving a person who is cruel or demands that people obey them completely, or who has extreme and unreasonable beliefs about race

fascism
noun [ U ] also Fascism UK ​ /ˈfæʃ.ɪ.zəm/ US ​ /ˈfæʃ.ɪ.zəm/
​
a political system based on a very powerful leader, state control, and being extremely proud of country and race, and in which political opposition is not allowed

Socialism is a left-wing ideology, political system or state-system. It is Marxist in origin. Some goals are equality, solidarity, peace.

National-socialism is right-wing ideology, political system or state-system. It is nationalist, chauvinistic, racist and fascist in origin. Some goals are inequality, war.

nationalism
noun [ U ] UK ​ /ˈnæʃ.ən.əl.ɪ.zəm/ /ˈnæʃ.nə.lɪ.zəm/ US ​ /ˈnæʃ.ən.əl.ɪ.zəm/ /ˈnæʃ.nə.lɪ.zəm/
​

a nation's wish and attempt to be politically independent
​
a great or too great love of your own country:
_{The book documents the rise of the political right with its accompanying strands of nationalism and racism.}

A very good "definition" for socialism is also "anything a right-winger doesn't like. Like health-care, Obama, pensions. But that is – of course – absolute nonsense. It is the destruction of meaningful discussion by Orwellian arbitrariness. Or are Roosevelt, Lyndon Johnson, Bismarck then socialists as well?

The mind of the Führer

To get that elephant named Adolf out of the way: he was an extreme nationalist, no socialist at all, influenced by Catholicism, capitalism, racism, antisemitism, social-darwinism (diametrically opposed to socialism or solidarity); and traumatised by World War I, lack of sex, lack of recognition as an artist. A simple conservative at heart, yet intelligent, but miseducated, who wanted to make a state of the past permanent by revolutionising the present. If that sounds schizophrenic, that's because it is.

Racism is essential to traditional national-socialism

So there is one misunderstanding in the question: you could not be a non-racist and be a national-socialist. Being a national-socialist means being racist as well, in fact at the very core.

The historic meaning of "socialism within national borders"

The historically exact meaning of a "nationalist socialism" is that a country is preparing/building communism but stays shy of world revolution, or attempts to advance in that direction without a world revolution on the far-far horizon, previously thought of a sine que non for communism. Communism here means a state made by the workers, for the workers and through the workers; that is the proletariat, the formerly lowest and biggest class of society. Justice in society by achieving equal opportunity and equal outcome for all. Abolishment of the very notion of different classes. Flattening of hierachies. By "socialising the means of productions" (machines, factories, land…). Lenin said that communism was soviet power (his word/concept/ideation for "democracy") plus electrification of the entire country. That means equal say in how things are run and progress for every last one village.

This is Stalin's "socialism in one country." Aimed at being able to survive as a model in one country (arbitrarily "this one now" – "national" in the sense of reach of power) until other countries can follow this brilliant example for a paradise on earth to follow suite. Work hard now to enjoy a bright and just future. Mainly left-wing, but with a heritage of born-in-war and avant-garde elitism resulting in yet another stratified state of classes, albeit with a comparatively flat hierarchy and little differences. Socialist core thought is "we all for a better future – we might have to change a few of how the things are run and done radically". The past was bad for most, let's try something better.

The genesis of the name "national-socialism"

The historically exact meaning of a "national-socialism" is that the German fascists adopted the Italian model but radicalised it even further into authoritarian and racist dimensions, especially anti-semitism. This is only "socialist" in just redefining justice for all as further cementing the class structure as being the optimal strategy for any society anyway. Any sharing of wealth in that system means dividing up spoils from plunder, whether enemies within the state ("Jews", "Disabled" …) or newly conquered people (other forms of "sub-humans" to enslave). Increasing levels of hierarchies. This was achieved by slightly restructuring capitalist production to being a loosely planned economy, planned in going by commando into the armament direction first, civilian consumption second. This is German national-socialism. Aimed at pleasing the immediate constituency and antagonise everyone else, as they are subject to subjugation anyway. "National" here in the sense of "this one nation is the best, inherently, forever." Work hard now to enable the perennial fight for dominance; the will breed the master race. The ultimate embodiment of right-wing conservative fears and hopes and goals. Highly dependent on ever increasing hierarchies, unquestioned commands and brutality, as the mere existence of mankind is a never-ending fight. Not only for one's own survival, but to ensure that for the annihilation of one's enemies. National-socialist core thought is "us good have to fight against them bad – we might have to discipline (kill) many (of 'them') so that everything stays as is." The past was glorious, let's try to go back there for the core features of society while keeping electricity for those who deserve it.
00

NATIONAL SOCIALISM as an intellectual movement emanated in the years 1926–28 from the brains of a few — chiefly north—German thinkers. As a political force it sprang from the mass-membership of the great Fatherland Party and the Pan-German Association. In a word—it was born of the annexationist militarism of 1917. In 1919 it became an independent political movement. Out of its raw material the Reichswehr in Munich forged a political weapon. This weapon was given shape in 1921 by Captain Ernst Röhm, and by a man of outstanding intellect but unstable character—Adolf Hitler. The movement derived its title from Hitler’s native Austria. It was adopted against the wishes of the present leaders and does not represent their political ideas. Those members of the National Socialist Workers Party who subsequently sought to give a literal interpretation to its title found themselves compelled by force of logic to leave its ranks.
_{Konrad Heiden: "A History Of National Socialism. Volume 2", Routledge: London, New York, (1934) 2010.}

The term "nazi" now and then

True national-socialists are properly called nazis.

True national-socialists are comparatively rare today. True national-socialists today are properly called neo-nazis, as the old guard is presumed to have died out with the German unconditional surrender in 1945.

The unfortunate drift or change in meaning to witness today is that the term "nazi" is somewhat watered down and even overused sometimes. A "grammar-nazi" might take great care for the proper use of rules in speaking a language, but despite a certain level a fanaticism there is not much reason to use this kind of language (this might be a case of "proper-meaning-nazi" on my side, alas).

We see a certain level of abuse of the term "nazi" that seems quite to inviting to label everyone one doesn't like and who appears to the right of one's own world views as "nazi". In the years following the total defeat of official national-socialism the term "nazi" only survived as a generalised insult against anything far-right, no matter how close or similar the actual concepts were or are.

In terms of analysing the political spectrum, one might think that there is a clear continuity from generalised right-wing to the extremes of fascism and national-socialism. If it weren't for the distraction of "socialism" in the name. But that is just a remnant of the origins of that far-right authoritarian movement. First, "Socialism" was the future, as seen by almost everyone after the Russian revolution and the end of the First World War. Some early members of the Nazi-party had indeed some rather left-leaning ideas about the future. But they were a minority quickly expelled. After 1934, as the real nature of national-socialist politics were put into practice, almost nothing remotely socialist remained. But the name stuck and was kept for social appeal as well as brand-recognition.

Essential differences between both ideologies: treatment of opposition

Enemies of "socialism" might have quite a hard time. Being called reactionaries, counter-revolutionaries, put into re-education. (Yep, historically there were also much harsher treatments. But the idea was betterment of all for the benefit of all. People were mostly just misguided, lacking class-consciousness. The mind is formed by material conditions.)

Enemies of "national-socialists" had and will have a hard time. Being called unfit, sub-human, inferior, lazy, saboteurs, put into camps for forced labour and extermination. (Yep, historically one could have a splendid joyous time in NS-Europe, as a nazi or member of the beneficiary races. But the idea was eternal battle and killing for the sake of it. If there were any benefits in it then in the form of honour, breeding success and dominance of power. People were born of the right stuff (nazis: blood; neo-liberals: inherited money). Essentialism, perpetually unchangeable. The mind is formed by inherited (pseudo-)biological traits, only ever so slightly mouldable.

Bad or not?

Whether any of the above descriptions, analyses or explanations amount to something "bad" is left to the reader. Apparently a huge range of people now enjoy being some kind of nazi. Thinking of it as the natural, id est biological way things ought to be.

As a working hypothesis I propose to ponder the following observation: almost exclusively far-right extremists ignore the actual history, deeds and politics of national-socialism and focus solely on the latter part of the term, socialism. In that world view the overwhelming similarities in actual political views and goals between "ordinary" far-right authoritarians and "national-socialists" should be overlooked by focussing on the distraction that the devil-be-with-us word "socialism" seems to provide.

The above does not mean that "socialism is good" or that both political systems cannot be compared at all, even some similarities between them found.

But labeling the nazis as socialists is either completely ahistorical, believing the fraud-by-misnomer the nazis devised or intentionally distracting from or even derailing meaningful discussion.

Update after question was edited and reacting to comments:

From 1920 to 1930/34 the national-socialists purged all socialism

You have to keep in mind that 'socialist' sentiments were later in name only! If these sentiments were identical in actual meaning to what actual socialists, anarchists and communists – or even liberals (European and American meaning!) – understood that term to mean than the NSDAP would have to be called a wholesale fraud on that account alone. They redefined these terms to suit them.

The early party programme of the NSDAP is quite slogan like in outlining actual plans and measures to be taken. The contents could be misidentified, and that was from the time that real socialist elements were driven out of the organisation, but kept with intention for working class appeal and brand recognition. That gave them some trouble for middle class appeal or pleasing their wealthy financiers when they still were trying to get votes.

The 25 points remained the party's official statement of goals, though in later years many points were ignored.

Point 3 for example (colonies!) was already thrown out completely when "Mein Kampf" came out, where AH switched his goals to Lebensraum. Point 4 ("no Jew can be member of the Aryan race") was followed through.

To make it clear that the economic concept of the NSDAP was neither anti-capitalist nor socialist, in 1928 he added to the party programme the statement that "in the face of the hypocritical interpretations of our opponents … the NSDAP stands on the ground of private property".
_{Avraham Barkai: "Das Wirtschaftssystem des Nationalsozialismus. Ideologie, Theorie, Politik 1933–1945", Fischer: Frankfurt am Main, 1988, p 32, fn 70. Citing: Otto Wagener: "Das Wirtschaftsprogramm der NSDAP" Eher: München 1932, p. 101–103.}

Der Fuhrer had dragged him around the new party palace and subjected him to one of his art speeches; when Scheringer wanted to speak of politics, Hitler had replied that the young lieutenant should believe and obey. Back in Berlin, Scheringer had complained to Goebbels of his experience with Hitler; he had asked the Berlin gauleiter whether the party still seriously intended to break down interest slavery? Goebbels replied: a breakdown could occur only to him who had to read 'Feder's nonsense', and when Scheringer argued that all this stood in the unalterable twenty-five-point programme, Goebbels cried in despair: 'I wish to God we had never heard of those miserable twenty-five points'.

That was the party's way with its most sacred principles! Even if the lieutenants were no more loyal to principle, many of them must have felt the same as the young officers of 1923, who had declared: 'It's all the same to us who marches; we'll march along!' (Meaning: and if Hitler doesn't, we march with somebody else.) But what if they had principles and believed in National Socialism? In both cases the practical result was perhaps the same. Scheringer sat in his prison cell and thought things over; the result of his thinking was that in March, 193 1, Hans Kippenberger, a Communist deputy, stood up in the Reichstag and read a letter from Scheringer. In it the imprisoned lieutenant renounced Hitler and declared himself a Communist: 'Only by smashing capitalism in alliance with the Soviet Union can we be freed,' he wrote. Goebbels wired Scheringer asking if he had really made such a declaration. Scheringer wired back: 'Hitler betrayed revolution declaration authentic reprint Scheringer'.

Konrad Heiden: "The Führer", Carroll & Graf: New York, (1944) 1999.

And really clearly showcasing the overly smooth transition from right-wing conservatism to nazism:

After the success of the NSDAP in the Reichstag elections of September 1930, there was a discussion about the integration of the NSDAP into government responsibility, Jakob Wilhelm Reichert of the "Verein Deutscher Eisen- und Stahlindustrieller" (Association of German Iron and Steel Industrialists) stated that the NSDAP had to give up "its half socialist and half foggy party programme" and work "in a truly conservative way".
_{Reinhard Neebe: "Großindustrie, Staat und NSDAP 1930–1933. Paul Silverberg und der Reichsverband der Deutschen Industrie in der Krise der Weimarer Republik", Vandenhoeck & Ruprecht: Göttingen, 1981, p. 76.}

As the money continued to flow from these circles to finance the party, we can quite safely conclude, that the conservatives were satisfied with the NSDAP being not socialist but truly "conservative enough".

Claiming that Hitler was a socialist would imply that he tricked all his backers and conservative friends and allies for years before he was given the chancellory – by the conservative president Hindenburg and his conservative circles of influence.

As socialism means also "socialisation of the means of production": Not a single Aryan capitalist was disowned. The programme point "nationalisation/socialisation of the trusts" is absolutely countered with the fate of the IG Farben. The poison gas used to kill the Jews was produced privately and the earnings and profits went into private coffers.

But this was all explained in more detail eventually to illustrate their self-image and desired projected image, while demonstrating the un-socialists' meaning of national-socialist:

Social and Socialist

"Yes, we call ourselves Socialist. That's the second step. The second step away from the middle class state. We call ourselves Socialist in protest against the lie of social middle class pity. We don't want pity, and we don't want social-mindedness. We don't care a hoot for that which you call 'social welfare legislation'. That's barely enough to kep body and soul together.

"We want the rights to which nature and the law entitle us.
"We want our full share of what Heaven and of the returns from our physical and mental labors.

"And that's Socialism!

Nationalist and Socialist

!Then we will prove that nationalism is more than a comfortable moral theology of middle class wealth and Capitalist profit. The cesspool of corruption and depravity will then yield to new nationalism as a radical form of national self-defense, and to new Socialism as the most conscious creation of its requisite preconditions.

This goes on to smear Marxism, Jews, Monarchists, Republicans, Internationalism, Capitalism or Parliaments, Pacifism, and solidarity, while at the same time outlining a still very capitalist corporatist state. These are not elements of socialism as it was understood then or understood now.

"Marxism will die, so that Nationalism may live! And then we will shape the new Germany – the nationalistic Socialist Third Reich!"

From the very handy Joseph Goebbels: "The Nazi-Sozi. Fragen und Antworten für den Nationalsozialisten", Verlag der nationalsozialistischen Briefe: Elberfeld, 1927/1932. (On archive.org)

Another prominent Nazi wrote this, but note the name and the date:

We therefore felt that the republican-monarchist semi-darkness deliberately maintained by the party leadership was a burden, the exaggerated reverence for the fascist authoritarian state, which is becoming more and more apparent on the part of the official party authorities, almost a danger to the movement and a sin against the idea.
Source: Aufruf der Otto-Strasser-Gruppe vom 4. Juli 1930: »Die Sozialisten verlassen die NSDAP« (The socialist are leaving the NSDAP)

At the very latest the Night of the Long Knives in 1934 marked the end of all even remotely socialist-like or revolutionary tendencies, ideas and people in the party.

The above is the answer. If you do not like to read too much, you may stop here.

As a highly upvoted comment demands a [citation]:

Genuine socialism, declared Hitler, meant to be an antisemite. Germans should be ready to enter into a pact with the devil to eradicate the evil of Jewry. But, as in his letter to Gemlich the previous autumn, he did not see emotional antisemitism as the answer. He demanded internment in concentration camps to prevent ‘Jewish undermining of our people’, hanging for racketeers, but ultimately, as the only solution – similar to the Gemlich letter – the ‘removal of the Jews from our people’.

But the Bavarian Reichswehr was to remain largely an independent variable in the equation of Bavarian politics in the latter part of 1923. And the part accommodating, part vacillating attitude of the Bavarian authorities to the radical Right, driven by fierce anti-socialism linked to its antagonism towards Berlin, ensured that the momentum of Hitler’s movement was not seriously checked by the May Day events. Hitler could, in fact, have been taken out of circulation altogether for up to two years, had charges of breach of the peace, arising from the May Day incidents, been pressed. But the Bavarian Justice Minister Franz Gürtner saw to it that the inquiries never came to formal charges – after Hitler had threatened to reveal details of Reichswehr complicity in the training and arming of the paramilitaries in preparation for a war against France – and the matter was quietly dropped.[…]

The struggle would leave only victors and the annihilated. It meant a war of extermination. ‘A victory of the Marxist idea signifies the complete extermination of the opponents,’ he remarked. ‘The Bolshevization of Germany … means the complete annihilation of the entire Christian-western culture.’ Correspondingly, the aim of National Socialism could be simply defined: ‘Annihilation and extermination of the Marxist Weltanschauung.’

The Bamberg meeting had been a milestone in the development of the NSDAP. The Working Community had neither wanted nor attempted a rebellion against Hitler’s leadership. But once Strasser had composed his draft programme, a clash was inevitable. Was the party to be subordinated to a programme, or to its leader? The Bamberg meeting decided what National Socialism was to mean. It was not to mean a party torn, as the völkisch movement had been in 1924, over points of dogma. The Twenty-Five-Point Programme of 1920 was therefore regarded as sufficient. ‘It stays as it is,’ Hitler was reported as saying. ‘The New Testament is also full of contradictions, but that hasn’t prevented the spread of Christianity.’ Its symbolic significance, not any practical feasibility was what mattered. Any more precise policy statement would not merely have produced continuing inner dissension. It would have bound Hitler himself to the programme, subordinated him to abstract tenets of doctrine that were open to dispute and alteration. As it was, his position as Leader over the movement was now inviolable.

Instead, the emphasis was placed entirely on the need to eliminate Marxism as the prerequisite of Germany’s recovery. By ‘Marxism’, Hitler did not merely mean the German Communist Party, which had attained only 9 per cent of the vote at the last Reichstag election, in December 1924. Beyond the KPD, the term served to invoke the bogy of Soviet Communism, brought into power by a Revolution less than a decade earlier, and followed by a civil war whose atrocities had been emblazoned across a myriad of right-wing publications. ‘Marxism’ had even wider application. Hitler was also subsuming under this rubric all brands of socialism other than the ‘national’ variety he preached, and using it in particular to attack the SPD and trade unionism. In fact, to the chagrin of some of its followers, the SPD – still Germany’s largest political party – had moved in practice far from its theoretical Marxist roots, and was wedded to upholding the liberal democracy it had been instrumental in calling into being in 1918–19. No ‘Marxist’ apocalypse threatened from that quarter.

Goebbels had been thrilled on more than one occasion in 1926 by Hitler’s exposition of the ‘social question’. ‘Always new and compelling’ was how Goebbels described his ideas. In reality, Hitler’s ‘social idea’ was simplistic, diffuse, and manipulative. It amounted to little more than what he had told his bourgeois audience in Hamburg: winning the workers to nationalism, destroying Marxism, and overcoming the division between nationalism and socialism through the creation of a nebulous ‘national community’ (Volksgemeinschaft) based on racial purity and the concept of struggle. The fusion of nationalism and socialism would do away with the class antagonism between a nationalist bourgeoisie and Marxist proletariat (both of which had failed in their political goals). This would be replaced by a ‘community of struggle’ where nationalism and socialism would be united, where ‘brain’ and ‘fist’ were reconciled, and where – denuded of Marxist influence – the building of a new spirit for the great future struggle of the people could be undertaken. Such ideas were neither new, nor original. And, ultimately, they rested not on any modern form of socialism, but on the crudest and most brutal version of nineteenth-century imperialist and social-Darwinistic notions. Social welfare in the trumpeted ‘national community’ did not exist for its own sake, but to prepare for external struggle, for conquest ‘by the sword’.

All quotes – and there are many more, not only in this book – from Ian Kershaw: "Hitler", Penguin: New York, 2013. Claiming that "Hitler was a socialist" is completely beyond reality.

He was not.

Just not.

In reaction to comments dobting the connection with Catholicism –– Just one example:

Derek Hastings: "Catholicism and the Roots of Nazism: Religious Identity and National Socialism", Oxford University Press: Oxford, New York, 2009. (GBooks)

This is an important book about the relationship between the Nazi movement and Catholicism before Hitler’s appointment as Chancellor. Derek Hastings argues convincingly that Nazism transformed in the mid-1920s from a political movement that was intricately intertwined with Catholic identity in Munich and championed the principle of Positive Christianity, to a political religion in its own right that was based on the messianic Hitler cult and practised pseudo-religious symbolic aesthetics. The significance of the book is to demonstrate for the first time in detail the existence of a Catholic-Nazi Synthesis that peaked in 1923.[…]
Hastings also provides further proof how right it is to emphasise the fluidity of the evolution of the Nazi movement, and also the fluidity of the religious identity of Nazi leaders and followers.
_{Review by Chris Szejnmann for HSozKult , 2012}

If you want to restrict your question to the strictest of laboratory settings, you may be able to squeeze out a point if the concerns are artificially limited to just economic questions about the division of labor. The problem is that National Socialism didn't happen within a laboratory, it happened in real life. Arguments made from the perspective of: "Perhaps a true national socialist wouldn't have done that" are a recognizable informal fallacy, and vulnerable to the pure fact that the actual National Socialists committed atrocities on a grand scale in the name of their total and complete ideology, whatever it may have been.

Trying to compare even in an academic sense policies or goals on a simple left-right scale may grant you knowledge at the cost of wisdom, so it is probably best to use it sparingly. Trying to split off "nationalist" or "socialist" in an attempt to understand why others simplify with the colloquial "fascist" I don't think will get you anywhere, but something that may help is to look into Horseshoe Theory. A quick summary is that far-right self styled "fascists" may actually believe in and support similar types of policies to those that may want to describe themselves as "anti-fascists." The only difference being who they choose to direct those policies against. This point of view naturally sits well with those in the "center" who just want everyone to get along, but your assertion that the "two sides" could "balance out to the middle" is a huge assumption that in the real world wound up with an estimated 3% of the entire world's population dead.

But to answer your title question: the full name of the party (in English) was: National-Socialist German Workers' Party, which you are correct itself includes appeals to nationalist, socialist as well as populist ideals, but in the end it's just a name. If you wish to promote policies inspired by both "nationalist" and "socialist" ideals, I would suggest you choose a different one. And yes they are bad.

Hitler originally joined the precursor to the national socialist party in 1919 as an agent of the Bavarian police to spy on them and make sure the weren't revolutionaries. At the time, they were significantly more socialist than the Nazis of the 1940s.

The Nazis shed much of their socialism around 1934 (when they killed George Strasser) in order to gain favor with industrialists and the "junker" military class. The socialist policies didn't help them much electoraly because most of the people they would have appealed to would prefer to vote social Democrat or communist. They didn't change the name of the party.

Some similarities between nazis and socialists --

Both Nazis and extreme socialists/(communist) believe in unlimited Government power.

Neither believes in individual rights. Specifically:

• No freedom of speech


• No right to a fair trial


• No freedom of religion


• No right to a meaningful vote


• No right to bear arms

The Nazis created a "cult of personality" type government where everything depended on a single leader. Extreme socialists/(communist) seem to do the same thing, while the less extreme ones generally don't.

Some differences --

Nazis wanted to conquer (and sometimes exterminate) other peoples by invasions and external force.
Socialists/communists usually prefer internal revolutions.

During the later part of their time in power, Nazis wanted to exterminate certain groups and peoples as a fundamental tenet of their program. By contrast, socialists/communists don't have a fundamental desire to exterminate this group or that, although there have were cases where they did so order to stamp out opposition.

Nazis were explicit about wanting to care for "members of the race" only. Socialists/communist generally claim to want to care for everyone. (Whether they actually do so is another matter).

Nationalism is all over the map. I don't think it has enough universal traits that you can say much about it in general, so trying to compare it with Naziism is probably a hopeless task.