The Soviet Union was "Socialist" with a "Socialist" economy ( transition from Capitalism to communism). The US was, and still is, a capitalist economy. The Soviet Union was controlled by national Communist parties (parties that believe in achieving a communist economy at some stage in the future) and by a "Supreme Soviet" representing each country at a central parliament, also controlled by the communist party of the Soviet Union.
The US was controlled by two political parties with right-wing conservative political ideology.