Russia was just one of about 14 'Socialist Republics" that made up the "Union of Soviet Socialist Republics" or USSR ("Soviet" is a Russian word which in context meant more or less something like 'Representative council'). Of course, like Serbia in Tito's Yugoslavia, it was the 'Equal among equals' that bossed all the other partners around at its whim, and for its own advantage. Being born a Russian was also a leg up on any Party or government job (To the extent there was a difference between the two), from lowest to highest, to the everlasting irritation of Belarussians, Ukrainians, and all the other players. It was additionally by far the largest of all the republics.
The traditional dividing line between Europe and Asia is the Urals, leading to references to 'European Russia' (Also known as 'Great Russia' for historical, cultural, and political reasons) vs. Siberia, the latter of which is basically Russia beyond the Urals. While there are a lot of resources beyond the Urals, around 90% of the people, civilization, tech base, and culture are on the west side of the mountains. The Great Russians don't think of themselves as Asians and never have, in fact that's kind of a slur to them because over there, that means you're saying they're Uzbeks, Khazaks, Azerbaijanis, etc., which are generally regarded by the Russians about the way we'd feel about Iranian hillbillies.