(1) Different people did receive different wages in the USSR, and managers even received bonuses if they met performance targets.
(2) “Communism” as defined by communist thinkers is primarily the state of existence where the means of production, e.g. factories and railroads, are universally accessible to everyone, rather than under private and exclusive control. This doesn’t really imply anything about government at all, and perhaps even presupposes the non existence of the state, which after all is claimed to primarily exist to mediate interactions between the classes.