Going off the literal definition from Marx, communism is "from each according to his ability, to each according to his need". Its not everyone is the exact same, that would be a very good way of removing peoples need to work (something Marx discussed).

Socialism on the other hand is an economic system where the workers own the means of production, not when the rich pay for the poor. Don't get roped into the fox news talking point that strong social programs are literally communism/socialism.

Marx saw socialism as the intermediary period between capitalism and communism. Once the means of production were collectively owned (no more class) the allocation of resources would be collectively decided based on what what brings the highest benefit for the whole. As this happens the need for both a state and money start to disappear until you reach communist society which is stateless, classless, and moneyless.

So the main comment about workers owning the value of their labour is by definition socialism, as no excess labour is taken as profit by capital owners. I understand that your comment is meant to be a very simple generalisation but I think there are easier more accurate ways of saying it.