They're the exact same except socialism is a more "watered down" version.
Definitions:
> Socialism is a political philosophy and movement encompassing a wide range of economic and social systems which are characterised by social ownership of the means of production, as opposed to private ownership.
> Communism is a political and economic ideology that positions itself in opposition to liberal democracy and capitalism, advocating instead for a classless system in which the means of production are owned communally and private property is nonexistent or severely curtailed.
In practice "Communism" means Leninism and its descendants, or occasionally revolutionary Marxism in general. No one reasonable would ever use it to refer to the likes of Olof Palme.
Definitions:
> Socialism is a political philosophy and movement encompassing a wide range of economic and social systems which are characterised by social ownership of the means of production, as opposed to private ownership.
> Communism is a political and economic ideology that positions itself in opposition to liberal democracy and capitalism, advocating instead for a classless system in which the means of production are owned communally and private property is nonexistent or severely curtailed.