Yes, that's one type of American.
Is an American someone who was born in America?
An American is generally speaking a citizen of the Untied States of America. They do not need to be born there.
There are also Native Americans. They are descendants of the indigenous people of North America.
You are defacto American if you are a United States Citizen entitled to a US Passport meaning you travel under American protection. There's no right or wrong way to be American. The United States is probably the most diverse nation on the planet and its' citizens come in all skin tones, languages,and religions.