Davros had it right: ownership is a key part of the concept.
Still trying to change the definition of a concept, using this forced semantic interpretation to support your position, I see.
newtype_alpha, the term 'socialism', as used by today's economists (and I'm really not interested in whatever fringe opinions you may want to dig up via google), includes various means of 'control' of the means of production.
Deal with it.
And, of course, there's no such thing as a pure capitalist state (nor is it desirable); various aspects are socialist in any country. That would be the social democracy part - it works quite well for providing a minimal standard of living, equality of chances (more or less) as long as the money for it are provided from somewhere else.