For a simple (but imperfect, as all are) analogy that should be familiar to HNers, the pre-USSR RSFSR is like the pre-Alphabet Google, the USSR-era RSFSR is like the Alphabet-era Google, and the USSR is to the RSFSR as Alphabet is to Google.

And “Soviet” as an adjective describes organs of the RSFSR, those of any of the other soviet republics that came to constitute the USSR, or of the USSR itself.