That is not the distinction between Socialism and Communism. Communism can be achieved via reform (theoretically), and Socialism can be achieved revolutionarily.

Socialism is Worker Ownership of the Means of Production.

Communism is a post-Socialist “Stateless, Classless, Moneyless society” achieved via abolition of Private Property.

Communism does not remove incentives for people to be able to improve their standard of living by working harder, this is just a false statement due to a lack of understanding.

Hope that clears things up!