The term American is used to identify a citizen or resident of the United States of America. The last word in the title gives the name. So, in reality anyone who is a citizen of the USA is an American and anybody else isn't even if they were born in some part of North or South America.
The interesting thing is that this is not true in other parts of the world. In Europe you have German, French, Italian, English, Swiss, etc., yet each is also a European. In the western hemisphere there are Canadians and Mexicans, and Panamaians, etc., and yet only those from the United States are Called Amercians.