Fascism in the most vague sense that you can get while still being accurate is enforcement of a hierarchy, practically no social mobility, based on traits like ethnicity, sex, wealth, etc. supposed to be the “natural order” of society; often involving some sort of mythological/religious/idealized “past” or predecessor society/civilization which was then upended by some sort of evil group(s) (the targetted groups/scapegoats), which stole from us and which are an evil that need to be stopped. This, of course, is slightly different from how Mussolini’s fascism was originally visualized – which was a corporatist nationalist dictatorship about “might”/the strong coming out on top (translated into militarism) justified by religion/mythology (in fascist Italy’s case about being the successor to the great ancient Rome and seeing through to a greater Roman Empire) – but it’s how the world has become to understand the concept of fascism as time went on.
This is the reason many see capitalism as sort of “diet fascism” – it’s entirely about a hierarchy based around socioeconomic class/groups, with highly restricted social mobility (although not completely closed off as fascism’s is), and it’s seen that your place in the hierarchy in a hypothetically purely capitalistic system is the natural order of things – your place in the hierarchy is supposedly based on how hard you work, rich people are rich because they’ve simply worked smarter and harder than the people under them, and anyone can go up the hierarchy if they simply just are a better person. Of course, in reality we know this doesn’t work and among other things generational wealth & systematic roadblocks created by the wealthy play a major factor in this hierarchy, but I digress. The reason classical liberalism / free market capitalism hates class equality, hates a system like socialism which calls for abolishing unjust hierarchies, is because it sees the abolition of the socioeconomic/class-based hierarchy as going against the natural order and forcibly placing people in the “wrong” places in the hierarchy (all on the same level) when some people deserve to be below others because they’re lazy, illegal immigrants, “criminals”, etc. In essence, they see equality not as equality, but as an “upside-down” hierarchy where the former upper class is forced below the formerly marginalized groups; to a more privileged person, equality feels like oppression. Capitalism needs an underclass to function, in a capitalistic system people with certain traits always have an unequal distribution throughout the hierarchy (scapegoated/marginalized groups significantly tending to pool at the bottom with only a few “token” examples truly traversing upwards, and people closer to the top of the pyramid being less and less prone to falling down the hierarchy). It sounds a lot like fascism, because fascism and capitalism are ideologies/systems with loosely equivalent structures but capitalism being far less pronounced.
Additionaly, classical liberalism & moreso conservative capitalism are centered around reggressing to a supposed “golden age” of the past where things were better before “they” ruined it (whoever “they” is and what specifically “they” did is vague and changes from belief to belief but usually includes taxation/redistribution of wealth/power away from the people at the top of the hierarchy, or some shift in the hierarchy). It’s like a much less pronounced form of the mythologized predecessor civilization/society of fascism, instead of hundreds or thousands of years ago it’s more like 30-40 years ago.
Fascism in the way we currently understand it doesn’t even strictly require dictatorial/autocratic rule, it can be enforced in a technically “democratic” system as long as certain groups are excluded from the democratic process. Of course, the line between democracy, broader oligarchy, narrower oligarchy, and autocracy becomes blurrier the more of the population you exclude, since democracy is more of a spectrum than anything, but generally there’s a lot of possible fascist systems where people would still consider it democratic enough. Your perspective is pretty deeply tied to which group you belong to as well – the average German thought Nazi Germany was a democracy even when Poland was invaded and throughout much of the war, but obviously the Roma and Jewish populace being genocided would definitely not agree. Capitalism does this exclusion to a large extent too – just usually not in the form of outright completely banning a group from participating – and the upper classes have signficantly more say in the democratic process, to the point where the upper classes can choose to completely eliminate options they collectively dislike enough from the equation regardless of the consent of the lower classes.
Overall while fascism and capitalism aren’t a complete overlap, fascism is for the most part a progression of capitalism (or, as more and more people see it, capitalism is a derivation of fascism and/or feudalism where we keep trying to patch up the flaws using a few socialist/progressive/democratic qualities) and pretty much requires a capitalist (or capitalist-adjacent) system to exist. Fascism can’t use, say, a socialist system because socialism inherently requires working towards the abolition of the power structures/hierarchies which fascism is based around. Of course, in fascist systems the supposed “superior” class often has power redistributed to them in the form of e.g. social welfare benefits and infrastructure investments, which isn’t straight up classical liberalism obviously, but that doesn’t necessarily violate capitalism/the capitalist power structures as a whole, it’s just using a different form of capitalism in order to keep the currently-not-scapegoated but also-not-highest castes content and thinking that things aren’t so bad.
If you have any questions about this or can’t see the reasoning of certain parts, I’m sure I (or someone else) will be happy to answer it for you.