Communism and fascism are alike. One has an international perspective, one has a national perspective, but the politics and control are very similar. They both exert control over the economy and culture. Interestingly, Lenin was more internationalist than Stalin. People don’t like hearing this because some still think communism is redeemable despite all evidence to the contrary.
China is a hybrid. Their roots lay in communism, but thru also draw heavily from Confucianism when convenient. Related to the last point, they do not share the roots of western philosophy, but rather eastern which makes comparisons difficult. That said, they claim to be die hard communists with Chinese values, as they put it.
I find it interesting that if someone on the right calls themselves capitalists or whatever, that’s taken at face value, but if someone calls themselves communists but they have some accompanying unpleasant characteristics it automatically disqualifies them as being true communists.
Their economic system is state sponsored capitalism but their government and everything else is communist.