Citizenship refers to something that happens as an automatic process of law, a right, with no forms required.
Generally, a person born inside the United States (and some of its possessions), is a U.S. citizen by law. There are a few exceptions to this, such as children of diplomats who would prefer to claim their parents’ citizenship.
Derivation (or acquisition) of U.S. citizenship occurs when a person born outside the United States to a U.S. citizen parent or parents can establish a claim of U.S. citizenship depending on the year they were born, their legal status at the time the claim is made, their parent’s previous residency in the United States, and other requirements.
Sometimes a person will be a U.S. citizen and not even know it. Being able to derive citizenship depends on a number of factors, such as which parent was a U.S. citizen, where the parent lived, and whether or not the child was born in or out of wedlock.
If you do not qualify for the automatic right to be a U.S. citizen, there is an alternative method to acquire citizenship called Naturalization.