Having grown up in the last days of the Cold War (I was in high school during the Reagan years), I can say the most obvious is the Individual vs. the Group. Politically, within the USSR, it was the group and people on the whole (at least theoretically) that mattered. The "state" and "country" were propped up to be the most important thing (although it was the people themselves that suffered in poverty), while in America, championing the individual and a strong personal philosophy to "sway the masses" is what made a business, strengthened a company (usually corporate) or got a politician or political party elected.
As a former figure skater and gymnast, I saw this firsthand, since some of my teachers had defected in order to live a "free" life, safe from the eyes of "the state" (very much like Big Brother) where they could live, work and espouse their own opionions freely with their personal creativity and humor, which had been watched over and heavily criticized before they left. They were told (and threatened repeatedly) with the mantra, "This is the way it has always been done. You are replaceable. We will get rid of you, one way or another, because you are all basically the same." Very harsh! America had (and still has) freedom of speech and the right to criticize a public official and their philosophy. Questioning those in power in the former USSR got you sent to backbreaking labor in the gulag, Siberia, or you were "disappeared" and your family members were threatened, since they were next in line should they disobey. Paranoia ran high, although those teachers took their training methods to American students (such as myself) and made us winners with shiny gold medals. Soviet/USSR and even today's skaters/gymnasts are usually teams and pairs, such as pair skating and ice dance, it is never one, while Americans will usually have the ladies or the men's event being the overall point-totalled winner. This philosophy, while not so "outward" today, still stands, all you have to do is watch these sports, and you will see the pattern.
The breakdown basically is: USSR/Soviet = Team philosophy, country, groups, The State. America = The Individual, Personal philosophy, individuality. Communism, though a failed concept, was supposed to be for the good of "all", whereas in America, it's supposed to be capitalist: the "perfect" person and standout individual with the right mindset, the "hard work" ethic, and the distinct characteristics of personality, fortune or simply luck is the one that rises to the top. The USSR officially fell in December 1991. It took them a few years to redo their flag and their anthem, while many former Soviets immigrated to the USA.
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