No, socialism is the end-stage of communism, which is just a transitionary period required for socialist-man to evolve. As one East Bloc joke went, "Mommy, will we still have money when we reach true socialism?" "No dear, we won't have any of that, either."
If you limit the definition of socialism to government ownership of the means of production, you've pretty much narrowed it down to communist implementations, since Germany's national socialists and Mussolini never completely got to that point in their planned economic development. You could argue that nationalizing industrial firms should count, but that's also common in right-wing juntas, monarchies, and other types of government, and it only encompasses a tiny part of the "means of production", usually the major revenue generators or critical infrastructure.