Both Capitalism and Socialism have room for public and private ownership, the difference is which sector controls the state, large firms, and key industries. The Nordic Countries are dominated by Private Capital, ie it is Capitalist, while the PRC is dominated by Public Ownership, ie it is Socialist.

Communism limits the personal freedoms of the bourgeoisie. All Communism is, is a more developed and global form of Socialism, where the small firms that once were private have all grown into the public sector or collapsed.