While to many there is no one who better personifies Fascism than Hitler, I have seen others make the claim that Hitler was in fact not a fascist. I know this is a difficult question to answer since Fascism seems to have a number of definitions depending on who you talk to. It's just interesting to see people make the claim that Hitler was not a fascist.
To give you the very short, un detailed answer, I think you can reasonably label Hitler a fascist in a casual sense, but there are enough differences between what Hitler believed and what traditional fascists believed to necessitate Hitler being labelled something differnet; very similar, but different.
You kinda identified the main issue in your question, fascism is a different thing to pretty much every scholar and every person it seems. It doesn't help that it seems like the word fascism gets thrown around to every dictatorship that isn't explicitly communist in origin. Furthermore fascism seems to have become a buzzword that roughly means "authoritarianism". This is all complicated by the fact that fascism is a very fluid doctrine, and the two traditional "fascist" dictators, Hitler and Mussolini, disregarded their own ideological convictions and did whatever the situation seemed to demand at the time. A key example would be Hitler's overt hatred of slavs and other inferior races, which was a key part of Hitler's political doctrine, yet when war time rolled around, one of Hitler's allies was Hungary. Hungary was a nation that Hitler was quoted as saying:
Even in Hungary, National Socialism could not be exported. In the mass, the Hungarian is as lazy as the Russian. He's by nature a man of the steppe. From this point of view, Horthy is right in thinking that if he abandoned the system of great estates, production would rapidly decline.
Fascism arose out of opposition to the Communists and the Liberal, Western democracies. Fascism has its ideological routes in the late 1800's, but it really in my view didn't become prominent, or really all that explainable until the 20's and 30's when people like Hitler and Mussolini began to actively spread the ideology, and the necessity of spread their ideology meant that they had to actually articulate their views. That's how we get things such as Mein Kampf, or Mussolini's Doctrine of Fascism (which is worth a read if you are interested in the development of Fascism, its free and relatively short in the link I provided).
In terms of similarities, there are enough between Hitler's National Socialism and Mussolini's fascism to, as I said in the beginning, label Hitler a fascist in a very casual, offhand way. Chief similarity, and one of the key factors in driving Mussolini into an alliance with Hitler was that both of their ideologies held roughly the same people in contempt. As I said above, Fascism and National Socialism were both violently opposed to any strand of socialism, communism, marxism, etc. and Liberal democracies. Both felt that these forces had resulted in corruption of the countries and a general shift away from strengthening the community, to strengthening the individual. In German ideology especially, the strength of a community was a central tenant of National Socialist and Fascist ideology. Of also striking similarity is the way in which the two men came to power.
Both Mussolini and Hitler's rise to power was very much tied to their respective ideologies and the fact that their ideology was fluid enough to not worry the largely conservative elites, while being perceived as revolutionary enough to combat the popular influence of the Socialists and Communists. That's why Fascism and National Socialism were both very popular among middle classes; Fascists allowed them to vent frustrations with Liberal Democracy and the current modern society, but unlike the communists and socialists, Fascists did not want to make any huge economic changes, and thus the middle class would have their cushy status in society protected.
In terms of war and expansion, both were very much believers in the idea that war was a good thing, that not only allowed vital territorial expansion, but warfare also allowed the men to show that they were truly loyal to the fascist state. Warfare also brought out the best qualities in men; things like devotion, duty, etc. Mussolini says in his Doctrine of Fascism essay that Fascism:
Fascism does not, generally speaking, believe in the possibility or utility of perpetual peace. It therefore discards pacifism as a cloak for cowardly supine renunciation in contradistinction to self-sacrifice. War alone keys up all human energies to their maximum tension and sets the seal of nobility on those peoples who have the courage to face it. All other tests are substitutes which never place a man face to face with himself before the alternative of life or death. Therefore all doctrines which postulate peace at all costs are incompatible with Fascism..... The Fascist accepts and loves life; he rejects and despises suicide as cowardly. Life as he understands it means duty, elevation, conquest; life must be lofty and full, it must be lived for oneself but above all for others, both near bye and far off, present and future.
No doubt familiar with Hitler's concept of living space in the east for Germany, you might be interested to know that Mussolini had a very similar concept in what he termed "vital space". This included territories seen as being Italian or rightfully belonging to Italy. This included Malta, Corsica, Dalmatian Coast, parts of Italy annexed by France, North Africa, etc.
Of course in terms of nationalism, both doctrines preach hyper nationalism. Mussolini's dream of rebuilding the Roman Empire and the idea of it being an Italian entity. Hitler of course had his fascinations with older German states like the Holy Roman Empire, and the idea of pure Germans who could act as role models.
Now there are for sure more similarities, but what muddles the waters, and the reason I said it is useful to label Hitler something else, is that there were some very big differences between the two.
A big issue is race. To Hitler race was vital to understanding society, history, and well, just about any issue really. Hitler's ideology preached that there was a strict racial hierarchy in the world. Aryan Germans were on top, followed by the Nordic races, then the Latin races (France, Spain,), followed by the slavs (Poles, Russians) and then finally the Jews. But to take a small detour, even here we can see how National Socialism's doctrine was bent by Hitler for pragmatic reasons, as the Japanese were made honorary "Aryans". Furthermore, to Hitler the Jews were responsible for the various forces that Fascism and National Socialism sought to combat; Communism was seen by Hitler as a totally Jewish invention.
Mussolini and Fascism on the other hand, were not inherently antisemetic or racist. Mussolini himself though very little of racially charged ideologies like Hitler, and once said that the idea that there is a master race was utterly stupid. And when Hitler and Mussolini met in Venice in 1934 to discuss ideas Mussolini found Hitler's ideas and theories to be lacking. Mussolini's Italy actually did a decent job overall of protecting Jews from Nazi Germany and in general Mussolini was opposed to racial legislation until he enacted anti-Jewish policies in 1938 to appease Hitler (going back to the idea that most fascist leaders tend to subvert their own ideology for pragmatic purposes).
In terms of the role religion would play in the state, the two also differed. Mussolini thought that Roman Catholicism played into the state and Italian nationalism, where as Hitler, while not opposed to having religion, was very much indifferent to it. Hitler also made sure that religious bodies would be totally subordinate to the state, where as Mussolini thought the state should protect the church.
Its also worth noting that Hitler did not think of himself as Fascist, and saw the fascist struggle as running parallel to the National Socialist struggle.
Ultimately its the race issue that truly keeps Hitler from being totally classified as a fascist, but there are other differences that also factor in as mentioned above. Just to reiterate, its not that Hitler can't necessarily be called a fascist, its just that (to quote every historian ever) more complicated than that.
If you are interested in something to read you might like:
Hitler, Stalin, Mussolini: Totalitarianism in the Twentieth Century by Bruce F. Pauley- I can't recommend this book enough, its does an excellent comparison of the methods and ideologies of the big three totalitarian rulers of the twentieth century.
The Fascist Style of Rule by Alexander DeGrand
If you give a word a novelty definition, you can prove just about anything. But often words have different meanings, and it's important to be careful about them.
The most narrow definition of "fascist" would be "a member of Mussolini's Partito Nazionale Fascista, commonly known in English as the Fascist party" in which case Hitler doesn't qualify, he led a different political party in a different country.
However, there's also the notion that the word "fascism" describes a certain type of political party: there isn't just the one fascist party, there are several fascist parties, just like there are several communist parties, or socialist parties or christian democratic parties, or whatever. In this generic sense, not only would Hitler's "National Socialist German Worker's Party" qualify, I suggest that it has become the standard and defining example. If you read people discussing fascist ideology, the Nazi party serves as the ultimate example of a fascist party, even more so than the original fascist party of Italy.
So, my counter-question to you is: who are all these people you mentioned who supposedly go around claiming that Hitler wasn't a fascist?
hi! hopefully someone can address your question directly, but meanwhile you may be interested in a few earlier discussions