That's the lie Stalin spread through the west using his agents and useful idiots in academia. There was never a smooth transition from a capitalist system to fascism, it required a coup or a civil war. If you look at today's China, it's a fascist state. They have a degree of market economy with strong state influence, just like nazi Germany. They've stopped using internationalism and class warfare as their core ideology, and went with nationalism, just like nazi Germany. They operate concentration camps to "deal with" religious and ethnic minorities, just like nazi Germany. They use their "glorious past" and racial superiority as a propaganda tool, just like nazi Germany. It was a gradual, smooth transition, not a revolution or a coup.
Yes, fascists and communists were mortal enemies, but because of their ideological similarities, not because their differences. They looked for support to the same group of people. In post-war Eastern Europe, the first ones communists dealt with were the social democrats. Not because they were the polar opposite, but because they were the competition. Btw, Mussolini was an editor of a socialist newspaper, before he ditched internationalism for nationalism.
The core of both is using the envy of gullible, working class people to gain power. Whether the target of this envy is jews or the bourgeoisie/aristocracy, is just a flavor. Realizing, that market economy (with strong state control) works better, than command economy, is the matter of time and intellect. And the choice between nationalism and internationalism is the matter of (geo)political realities, a foreign policy tool.