> Former USSR countries are mostly unified by the same language, religion (or lack of) and culture
You are a bit wrong there. Consider the Baltic states: Estonia, Latvia and Lithuania. Culturally, genetically and linguistically they have almost nothing in common with their USSR neighbours. And pretty much the only thing share by the three states are the geographic location, some common lineage, and the fact that they were part of the USSR for about 45 years.
For example, Estonia considers itself to be a Nordic country; its inhabitants are genetically Nordic (and often as blonde as Scandinavians) compared to the Balts of the other two states, and its language is closely related to Finnish. (During Soviet occupation, the Estonian language was dominated by Russian, which was made compulsory in schools; after the USSR collapsed, Estonian has blossomed, especially among youths; I believe the same thing happened in the other Baltic states.) Latvian and Lithuanian share a common linguistic heritage, but they are different, and Latvians and Lithuanians cannot understand each other (unlike, say, Italians and Spanish people, or Scandinavians). Genetically Latvians and Lithuanians are closer to Estonians and Finns than to Russians.
The Baltics is just one example. For examples of other countries that seem weirdly out of place in the traditional US image of the Soviet Union, look at the Central Asian ex-Soviets states, such as Tajikistan, Kazakhstan and Uzbekistan.
> They used to be the same country
The Soviet Union was a union of countries -- many of them forcibly invaded and taken over by the Soviets in the wake of WW2 -- and everything (culture, language, religion, etc.) reflects this fact. The Soviets ruled everything, including the economy, from Moscow, but each of the member states very much preserved their own sense of identity; it was a union, but not a "unified" one. While the Soviet Union may have superficially resembled the US, it was always a very different beast.