I can not think of a country that does not have a mix of private and public ownership of production/distribution. What should we refer to those countries as?
government does not equal socialism. Socialism is against private ownership of the means of production - an economy that permits private ownership of the means of production is capitalist. The few industries that are nationalised are not held in common by the people and managed democratically - they're owned by the government who try to manage it the way they think the people would want it. That's what's commonly referred to as state capitalism.
And capitalism is against public ownership of the means of production. Any country that does both, has an economy that is neither purely socialist nor capitalist. I personally would not want to live in a purely capitalist, nor a purely socialist state.
(Sidenote: State capitalism and market socialism are essentially the same thing)