There's a little more to it than that... but what most people ascribe as "fascism" conflates with authoritarianism, which includes the political and economic structures the people talking or using the "F" word generally do support.
There's no communism that doesn't lead to authoritarianism, for example. Which leaves the distinction about economics.
>>There's no communism that doesn't lead to authoritarianism
Unless you believe this because "there's no State that doesn't lead to authoritarianism (based, dope, great take)" saying "this thing is actually the exact same as a thing that is literally the opposite of it" is just whataboutism.
These takes are weak. Here's what I think fascism is (based on like, studying words and theory and philosophy and shit, and not just trying to stunt on my political opposites): It's a far-right, ultra-nationalist, violent, authoritarian world view that SEEKS centralized power and openly opposes liberal and communist parties where it is erected. By design and declaration it seeks to promote violence, masculinity, and a national rebirth to a bygone era lacking in modern decadence.
All this is to say, if you're an Anarchist (hi brother!) seeking to scold the commies for not being Left enough, save that for after the revolution. And if you just want everyone to equate commies with fascists because "then both bad" because you're Right of them, get better at rhetoric.
There's no communism that doesn't lead to authoritarianism, for example. Which leaves the distinction about economics.