National Socialism is an aspect of fascism, but fascism is not an aspect of National Socialism. What I mean by this is that although Nazism is considered to be a form of fascism, it is usually considered an extreme form of fascism. This is because in the 1930s and '40s there were many fascist parties in most countries throughout Europe, and some around the world, many of which were also in power, but none of these fascist parties and governments were anywhere near as extreme as National Socialism became, and it is for this reason that many historians consider National Socialism to be an extreme form of fascism, and some historians even argue that it's not really fascism but something that's beyond fascism, something more than mere fascism. 

 

"The aim of the Nazis was not the establishment of German supremacy, although they occasionally referred, for mass consumption, to that goal. The aim of the fascists was the establishment of the master race." Noel Ignatin, “Fascism: Some Common Misconceptions,” 6. 

 

Hitler envisioned his National Socialist movement as encompassing three main goals – first, Hitler wanted a classless society among its leaders to be based on “front solidarity” (Hitler's definition of socialism) and on meritocracy. Second, he did not wish to be limited to one class or society but rather to be all inclusive within the German or the Aryan race (social Darwinist). And third, whereas Marxism sought to brake down class structure in society – Hitler wanted to enshrine it. 

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This website considers primary and secondary source materials and what these sources have to say about the question, "What Is National Socialism?" 

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Why do some people confuse National Socialism with Socialism?

"Were we to accept self-declared nominalisms uncritically we would have, for example, to categorize the Nazis as members of the socialist community because they called themselves national socialists. That would, to put things mildly, stretch any reasonable understanding of interwar fascism beyond plausible limits. That is why self-definition by an individual or group—though unquestionably paramount in any investigation—must be tested against a range of perspectives that emanate from outside those engaged in labelling their own ideational wares."

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Michael Freeden, Liberalism: A Very Short Introduction, 70. 

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"There are sufficient similarities between Fascism and Nazism to make it worthwhile applying the concept of fascism to both."

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Kevin Passmore, Fascism: A Very Short Introduction, 62.

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