Both words are complicated, debated, co-opted, etc., so it’s hard to come up with a definition and relationship that’d be universally accepted. But Socialism, broadly speaking, is the ownership of the means of production (things that, when work, generate money like factories, etc.) by the workers. Different variants of socialism call for that ownership by different means, usually either by a government as a proxy for the workers, or by industrial unions, or by the workers’ directly.

Communism is a variant of Socialism that, broadly, assumes that socialism will eventually progress to a classless and stateless society.