Nazism is fascism. It’s the softer sell because if gives the pretense of private ownership. Communism gives no such pretense. Both however are utterly evil, totalitarian systems.
Fascism is Fascism. Nazism is Nazism. Hitler and Mussolini didn’t even get along.
Actually there was private ownership under Communism, at least for a short period....
https://en.wikipedia.org/wiki/New_Economic_Policy