Fascism as an ideology is basically a counter cultural reaction to liberalism and democracy. It's an ideology that emerges in countries who for one reason or another seen democracy as a failure and whose goal is to return society to an era of absolutist control where the state with a strong dictator on top controls all ostensibly for the benefit of the people. In effect, the ideology idealizes the concept of the "benevolent dictatorship" and seeks to establish one. In that respect its closest cousin ideologically is the Roman Imperial system of late antiquity and the concept of respublica where the emperor had absolute power but also a duty to use it wisely rather than anything modern.
In practice of course once you hand anyone absolute power it just devolves into another generic pragmatic dictatorship like Tsarists Russia or pre-revolutionary France where keeping and maintaining power becomes the only goal. But reality always does have this annoying tendency to ruin beautiful theory with ugly facts.
National Socialism on the other hand is a completely different beast. The movement started off a branch of anti-globalist democratic socialism in the 1920's in Czechoslovakia as a reaction to the at the time dominant International Socialism. And at the time it was actually quite reasonable.
You see, when Marx postulated his version of Socialism he called for it to be a worldwide international movement. International as in he and his followers wanted to stage violent revolutions in every country in the world and cover the entire planet in a thick red blanket of dictatorships of the proletariat whose streets would be paved in the corpses of the rich and nobility. This view while quite extreme even to the stuff we hear from the modern radical left attracted a lot of people however because a lot of people were poor, overworked and disenfranchised. And the idea of taking over the world and establishing a system by the people for the people built on a foundation of the dead bodies of those that kept you down sounds quite nice when you are in that position. This is why the early communist movement tended to thrive in places like the collapsing Russian Empire or the collapsed German Empire and why Europe has a long and complicated relationship with anarchist bombers.
At the time and especially after WW1 Marxist socialists actually despised and clashed with not just the right wing but also democratic socialists whom they saw as sellouts. Which, quite naturally would have produced a backlash. Newer the less, things could and did get worse and they did. After WW1 and the Russian civil war the Soviet Union started funding and "advising" communist parties around the world and especially in Europe. See the Spanish Civil War for how nice that went. So that by the 1920's the fear wasn't just that if your local communist party won they would paint the walls red in capitalist blood but that once they were done they would turn your country into a mini Soviet Union or worse a Soviet puppet state.
And that is where Hitler enters the scene. Every society that is in a collapsing state such as the 1917 Russian or 1920's German states produces both right and left wing extremists. The former are the sort of insane world revolutionaries I described that would eventually give us such nice and friendly people like Stalin, Pol Pot and Mao. The later are ultra-nationalist ultra-racist fanatics that think all social problems can be solved by just killing off or enslaving anyone who isn't a part of their preferred racial or ethnic group.
These two groups hate each other primarily because they both want absolute power rather than anything else. In Russia, their clash produced a civil war. And in 1920's Germany things were not looking much better with pieces of the country actually having their own
mini communist revolutions that only ended when ultra-nationalist militias made up of former war veterans discretely armed by the central government marched in to fight them in the streets. So yea, bad times.
Both groups however do have a common point in that they both see liberal democracy as a failure and want to establish a dictatorship ostensibly for the benefit of the people. What Hitler realized is that he could use this common thread to combine the two radical movements based around this concept of a "benevolent peoples dictatorship" if only he combined the worst aspects of both. And in doing so he turned German National Socialism into an unholy spawn of the two with him self on top as its god-king.
Which is to say essentially a radical communist movement that takes cues from ultra-nationalism to claim that whilst the workers are indeed oppressed and should go murder all the "evil" capitalists it's only the non German capitalists that are actually evil. German capitalists are good and proper and would newer oppress the worker because they are both German. And if they are doing that it's only because otherwise they couldn't compete in the market with the "evil" foreign capitalists or pay their loans to the "evil" foreign bankers. So clearly, the solution is for the workers of Germany to conquer the world, murder all the non German capitalists and take their stuff to give to the German capitalists who will than control the means of production for the benefit of the German race. Everybody wins, as long as they are German.
And if this sounds plainly evil that's because it is. Very smart and manipulative yes, but also plainly evil. It is however very different from Fascism. Indeed, the two only really worked together because of circumstance rather than any ideological alignment. Franco wanted help anywhere he could get it. And both Japan and Italy wanted territories that were controlled by the allies so it made sense to side with their enemy. If the territorial situation had been reversed both Italy and Japan could easily have fought on the allied side.
A funny sidenote to all this is that with Hitler removed from the timeline National Socialism would most likely have not turned down the route that it did and would have instead remained along the Czech model of just being a benign version of anti globalist socialism. A sort of "lets build socialism at home for our own people and the workers of the world can fend for them self" sort of idea which even today has relatively broad appeal and would thus possibly have become and remained significant element in modern democratic socialist societies such as those of western Europe. And rather than becoming a bad word in the world of Command and Conquer with an aggressive expansionist Soviet Union looming over Europe it would likely have become the only acceptable form of Socialism in western society. Which is a funny thing to contemplate, you must admit. Like, can you imagine having a conversation and saying:
"No, he is a nazi. Those are the good socialists." If nothing else it boggles the mind.
It's one of those bad jokes history makes by showing us how one man at the wrong place in the wrong time can do so much harm.