Generally speaking, U.S. citizens have only two broad categories of rights/privileges noncitizens have not:
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Right of residence on U.S. soil. If you’re a citizen convicted of a felony the state can imprison or even execute you, but it can’t deport you. Exile is a punishment unknown to American law.
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Political participation – voting and holding public office. Not quite so cut-and-dried – even foreigners have their free-speech rights and can volunteer for election campaigns; and not all citizens can vote or hold office (you might be barred by a past conviction for crime).