Am I "Black" or "African American"?

No it’s not. It’s because black/African American people collectively use more than one designator to describe themselves and the people who wrote the form are trying to be inclusive. Some people identify as black, and others identify as African American, some people identify as both, but it’s all the same thing. An African-descended Ethiopian immigrant who is not a citizen could call themselves African American, and the identifier is the same. A European-descended/white South African immigrant who is currently a citizen is not African American.

It’s a racial identifier; it has nothing to do with citizenship or nationality.