Australia a communist State, page-459

Your definition is the classic text book explanation but in practice all communist states use a much wider definition

They have state controlled private business in China but Russia was a different story

What are the practices of communism?
These governments were characterized by one-party rule by a communist party, the rejection of private property and capitalism, state control of economic activity and mass media, restrictions on freedom of religion, and suppression of opposition and dissent.