[объясняю нерусским людям, в чём разница между Россией и Советским Союзом, и причём тут (к примеру) Грузия. Вам - неинтересно. Ну разве что неточности найдёте.]

There was a Soviet Union (a.k.a. CCCP - SSSR, a.k.a. USSR - Union of Soviet Socialist Republics). It was consisting of fifteen republics, one of which was Russia. Among the others are: Georgia, Ukraine, Belorussia, Lithuania, Latvia, Estonia, Turkmenia, Armenia, Azerbaijan and so on. Formally, all republics were equal, but the informal (but clear-to-see) leader was really Russia (it has the biggest area; official USSR language was Russian; the capital of USSR - Moscow - is also the capital of Russia). Also, five of those republics were under the Russian Empire (before the 1917’s revolution).

This is probably the reason why people from USA called “that other big country” Russia. The other reason can be political. But that was (and is) really really wrong - Russia is definitely not USSR, like New-York state is not the USA (but rather just a part of it).

Since 1991 the USSR is no more. So instead of fifteen republics there are fifteen independent states. All these states can be referred to as ex-USSR. But, for example, Georgia can’t be referred to as ex-Russia now. And even in USSR times Georgia was not the same as Russia (as Los Angeles is not the same as New York).

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