The main difference is who owns the means of production. In communism, the government does. In socialism, the people do.
What would we call a hybrid system in which the government is made up of the people and owns the means of production? Direct Democratic Communism?
Edit to add:
A federation (also called a federal state) is an entity characterized by a union of partially self-governing provinces, states, or other regions under a federal government (federalism). In a federation, the self-governing status of the component states, as well as the division of power between them and the central government, is constitutionally entrenched and may not be altered by a unilateral decision, neither by the component states nor the federal political body without constitutional amendment.