The concepts of nationality and citizenship are taken for granted by most people, but the existence and sense of such concepts is contingent on history and non-unique. Historically, people have generally either lacked them or understood them differently than we do today. And even today, different concepts are extant. The Soviet/post-Soviet concepts differ from that prevalent in, for example, the contemporary United States.
When Lenin took power in 1917, the Soviets wanted to be the most politically advanced society of their day, and to do everything that was considered "enlightened." One of those things was "national self-determination," and Lenin was initially inclined to dissolve the Russian Empire and give its peoples their own political space. Of course, this was mostly nullified by the Bolsheviks' dictatorial ideology, but it did lead to a certain administrative autonomy for the fifteen "Soviet socialist republics," including a larger role for local languages and sometimes a revival of respect for local historical heroes. One of its effects was to recognize everyone's "nationality."
A Soviet or post-Soviet passport records a person's "nationality": Russian, Chechen, Jew, Kabardinets, Buryat, Georgian, Tajik, Ukrainian, etc. The nationalities are more numerous than the republics, and one's nationality is not determined by where one lives: there are Tajiks living in Uzbekistan and Uzbeks living in Tajikistan, for example. Passports are more important in post-Soviet countries than here. In the United States, people only get passports to travel abroad. In post-Soviet countries, passports serve as a form of ID internally, like driver's licenses, and in principle the police can ask you for your passport at any time. There are zagran pasporty, "foreign" passports for travel abroad, and vnutryennye pasporty, "internal" passports.
With the exception of the Baltic republics, and now Georgia, citizens of former Soviet republics can travel visa-free to Russia. Lately a lot of migrants have been coming to Russia to work, since wages have been rising so fast and labor markets are so tight. Once here, they lack rights-- Russians don't enjoy rights the way Westerners do, either, but migrants are treated much worse-- and they face discrimination, but it still seems to me that the society is able to accept them in its own way because of the attitudes towards nationality and citizenship inherited from Soviet times. After all, there are already a lot of non-Russian citizens of Russia. A migrant worker from Tajikistan, provided he speaks Russian, isn't all that different from a Russian citizen of Tajik nationality, or of Buryat, Tuvan, Kabardinets, Kazakh nationality, etc.
The American concept of assimilation and equal rights has a moral advantage in that an immigrant has, certainly as an ideal and largely in practice as well, the opportunity to become "just like everyone else." He can, and certainly his children can, do or be anything that any other American can. Russian nationality, on the other hand, is theoretically inaccessible. On the other hand, Americans' psychic-ideological need to give everyone equal status means that if we don't feel someone is fit to earn that equal status we are compelled to try to shut them out altogether. If a Tajik gets to America, he is on the path to being an American citizen/national (no distinction between those two concepts for us) with equal rights, which he can't be in Russia, but his chances of ever getting to America are virtually nil. This exclusiveness vitiates, or perhaps nullifies or inverts, the moral advantage of America's belief in equality for the favored few who get to be citizens. There is a sense, then, in which Russia is a more open society than America. The average Western citizen, or journalist, or politician, knows nothing of this, both because he doesn't know the facts-- even the basic fact, one of the most morally important in the modern world, that the vast majority of the human race is excluded permanently from American territory by birth, is unknown to most Americans-- nor has he reflected upon the theory.