Oh, and it can get more complicated. My parents are both U.S. citizens born in the U.S. Daddy was military. One of my sibs was born in France in the fifties, one in Germany in the 60s. The one born in France is a naturalized citizen and could have opted for dual citizenship, French or U.S. when she reached her majority. Because my parents realized we'd most likely do another tour overseas somewhere, some time, they opted to take her in and make her a U.S. citizen (high cold war days; you really wanted all your kids to be U.S. citizens so getting them out of the country in an emergency wouldn't be a problem). My other sib was born in Germany and was a U.S. citizen from birth and is not a naturalized citizen.
Someone once told me it was because Germany was still considered occupied when when the kid was born there, hence a U.S. citizen. The other was in an independent country, so not. He wasn't anyone whose word I'd trust, but there is a sort of convoluted reasoning to it. There is also something called "status of forces agreements" between the U.S. government and any foreign government where we have an installation, and it can vary greatly from country to country.