To understand China you have to understand the three socialisms. And you also have to understand that no matter a country's ideology or intent any socialism will end up implementing mixture of the three socialisms even if they claim to only be one of the three.

Communism - Socialism by state ownership and control of all means of production
Fascism - Socialism by acceptance of inequality and acceptance that people have unique rolls to carry out in life. AKA Class socialism.
National socialism - Defining the social creature on ethnic lines. All socialism prioritizes the well being of an anthropamophized abstract conception of "the people" over actual people. National socialism defines the edge of that creature on ethnic lines.

All real world cases of socialism end up implementing some mixture of all three. The Soviet Union did in fact care about Russian interests and were willing to violate the communist objective of feeding everyone (rip Ukraine) to prioritize Russian needs. The soviet union also had people take on different unequal rolls in its actual operation. Class was a huge part of the Soviet Union.

So the question of analizing any socialist country is not to categorize which one they are, but to rank how much they are of one verse another.

China is willing to temporarally, but also indefinately, forgo state control of capital because they view that as what is needed to serve their ethnic interests in the moment. They are not shy about stating it in those terms. They also very openly accept unequal rolls. So China is in order:

National socialist
Fascist
Communist

They are all three. That just happens to be that order even though they don't view themselves that way. They are actually pretty close to zero on the Communism scale as a matter of management, but are politically communist because their ideology is full of communist dogmas. But ideology and policy are different things.

Cuba though is Communist,Fascist,National socialist. I rank their Communism above their Fascism because they actually do have state control of production which is rare, and they don't have a significantly sized caste of betters. It does exist but is pretty small. It's going to exist to some extent but it is guarenteed to exist to some extent. They are low on national socialism because they don't express very much ethnic interest, but I'm sure it exists.

BTW the NSDAP wasn't purely uncommunist either. The same rules apply to them. To AnCaps like myself everyone else looks like a commie. And the NSDAP is no exception. Any socialism requires some state control over production, just as any socialism requires unequal rolls, and any socialism requires some definition of who is us vs them. This is why all instances implement some mixture.