Sure, I agree.
In the case of former Soviet Union, I was talking more from an ethnicity standpoint. All Soviet countries included Slavic people, except for the Baltic ones.
So I meant that you can associate Ukrainians and Russians in that they're both Slavic people, whereas Baltic ones have different roots.
The Olympic vs "People's" denomination issue is very complicated and one should start to speculate from the very start:
<<What defines a nation/country?>>
It is very hard to tell. It can't be language, it can't surely be current borders (they can change easily), it can't be ethnicity either... Counterexamples exist in all of this cases.
I see you're from Japan and I'm not an expert in your country's history/culture, but maybe it's the only case (at least off the top of my head) of a people that can be defined easily with one language, one ethinicity, one common history/culture) (being an Island surely helps).