Also, I'm a foreigner.
From your nick, I'm presuming you are a Ukrainian citizen. The concept of "federation" you are familiar with -the present Russian Federation- for example, are at the same time much looser and much more rigid than the United States' federation.
Why the paradox?
First, the states of the United States cannot leave the Federation. The reason Abraham Lincoln is on Mount Rushmore, and on the US 1-cent coin is that he defined the doctrine that a state may not secede from the Union, and any attempt will be suppressed with the full force of the Union. There are people who pertend and posture otherwise - as happened after Obama was re-elected, but that is the true fact.
Second, there is no distinction between the states in terms of application of federal law. There is absolutely no restriction on movement of goods, services, or individuals, between states; no papers are required; borders are marked only with large billboards which say "Welcome to ___" (and spend money while you are here). The only exceptions are, in some places, inspection of live animals, fruits or vegetables to reduce the chances of the spread of diseases.
What there is, however, is differences in business climate, state taxes on corporation and individuals between the states. This means that both people and corporations will often choose "nominal" home states, and do business in other states. That's what the Wyoming incorporation is about.
