[vacri]

So why did the Soviet Union have private housing (and the ability to inherit it)? Why does the modern USA have public lands, managed by the government for the free use of all? How do you classify Chinese communism?

It really isn't an either/or proposition; you're only taking the absolute extremes of the concepts. If it was such a proposition, where does the switch take place? At what point would a nation 'flip' from being 'socialist' to being 'capitalist'?