I've wondered that too, and from what I can understand, the distinction is that the Russian Oligarchs don't just have political influence, their wealth itself was a result of political connections with the ruling elites from the start.
https://kamilkazani.substack.com/p/avocado-economy-why-russi...
The "America bad" crowd is so eager to say they're all the same that they intentionally look away from any nuance.
Not all American super wealthy are oligarch but some are very close to the mark. Borderline cases that are concerning: Elon Musk is an American oligarch. Bill Gates is an American oligarch.
Also can someone dump 4Gs of Google’s codebase somewhere?