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.
Seems relevant considering “The Federation”.
Not quite as simple as checkboxes, but the ability is there to some degree!