I think fascism is a better description of the examples you refer to - which is basically a more extreme and formalized version of “crony capitalism”, where politicos and corporatists coexist in a symbiotic relationship.
The Soviet Union was much closer to the ideal of communism where private ownership was essentially non-existent.
i suspect that the Chinese leadersip would probably say that they were at the Socialist state, rather than then Communist one, so they could afford to be economically pragmatic. But I digress.
It seems to me like China’s economy is basically a hybrid or combination of Socialism, and de facto Fascism. But that’s just my opinion.