ok so, i think people confuse the idea of communism, with the concept of lefty communism. There are two types of communism. True blue communism, early soviet union for example. And then what i like to refer to as "pseudo communism" later soviet union, and most other communist states, including china. Most people advocate for a more "true blue communism" which is a different thing.

secondly, most people like to compare between capitalism, and communism, with socialism being somewhere in the middle, where as i think it's much more accurate to summarize it separately. You have capitalism which is a big player, socialism (communism doesnt count), and then you have authoritarianism. Generally, as a state you exist somewhere in this triangle of economic ideals. You either have a relatively free economy, under capitalism, a collectively owned economy under socialism, and then a centrally owned and planned economy under authoritarianism.

The problem here is that china is more of an authoritarian capitalist state, than it is communist. It doesn't subscribe to any of the main tenant of communism as is blatantly evidenced by their society. However it does have more authoritarian polices, as evidenced socially and economically.

German nazism was actually done under the socialist party, the funny left leaning one. Fascism itself is apolitical, it doesn't care what side of the spectrum you're on, for example stalin might be considering a left leaning fascist. Generally fascism uphold right wing ideals as they tend to be the most simplistic, but that's more of a secondary force.