You're thinking of Capitalism and Socialism as Private Property and Public Property, and as oil and water. That's not how systems work in the real world, however. An economic system is determined by what is primary in an Economy, and at scale property relations are entirely mixed and inter-related. Having safety nets doesn't make the Capitalist EU somehow "a mix," and having markets doesn't make the Socialist PRC Capitalist either.

You are partially correct, in that markets are a useful tool at lower stages of development and public ownership and central planning at higher stages, but that doesn't seem to be where you were going with that.