Socialism was and is at its core about the working class as a whole owning the means of production, becoming the only social class in existence and in effect ending the cycle of class struggle that has defined human history for the past few thousand years (at the very least since Marx & Engels first formulated scientific socialism. Utopian socialists had similar visions of a future society but usually lacked the framework to clearly articulate their criticisms of existing societies).

The term Communism, although used since the XIX century, became mainstream in the XX as a reaction against the perceived reformism or capitulation against capitalism of the then-called "socialist democrats" of the Second International. Technically, though, Communism only means the end-goal of the socialist struggle, again a classless society where everyone works according to their capacity and receives according to their needs (see 'The Critique of the Gotha Program' by Marx, or Lenin's 'State and Revolution' where the distinction between the revolutionary transitional stage and the classless, stateless end-goal of Communism is clearly made. Yes, Lenin thought a society without any State at all was desirable). The fact that States ruled by Communist Parties implemented imperfect versions of socialism, or had any number of problems small or big, in no way should make you pretend that the definition of Communism is "the government owns everything". Or, much worse, that it is in some sense just the same thing than Fascism. This makes no sense historically or theoretically, and is about as accurate as pretending that parliamentary democracy in industrialized nations is at its core all about spending 10% of their GDP in weapons and bombing the shit out of third world countries.