Davros had it right: ownership
is a key part of the concept. Mainly this is because varying levels of control exist even in capitalist economies, from absolute control over what is nominally a privately-owned company, to ordinary business regulation or restriction. Governments can and do -- and really, MUST -- control their economies to a smaller or greater extent in order to maintain stability. Even fascists and totalitarian regimes often permit private ownership of key industries as long as the owners continue to play ball.
Government OWNERSHIP of the industry is another matter altogether. State-owned companies and institutions need not be under the direct CONTROL of government ministers and could just as easily be delegated to local officials and run on a for-profit basis anyway; the fact that the government and NOT private investors own those resources is the difference between capitalism and socialism. In some ways there is a bit of an overlap between dictatorships and socialist regimes, but only insofar as socialism is a useful but hardly inevitable tool of dictatorships.
Broadly: Capitalism is an economy whose means of production are owned by private capital. Socialism is an economy whose means of production are owned by government institutions.