Both sentences are correct, Crotalito. He wasn't asking for a correction. He's asking if it's OK to call himself an American.
The noun American has been used since 1580, according to some sources. It originally described the 'native American' discovered on the American continent.
Since then, three different meanings have evolved for the noun.
The first meaning listed in every dictionary I checked is "A citizen of the United States of America." The second meaning is "A native or inhabitant of the Western Hemisphere." The third meaning is "An Indian of North or South America."
So, when we citizens of the U.S. call ourselves Americans, we are simply using the first meaning given in the dictionaries of American English. When people other than citizens of the U.S. use the noun to refer to themselves, they are simply employing one of the other two definitions.
I think that those who are offended that we in the U.S. refer to ourselves as Americans should check the dictionary. They'll see we are employing the noun correctly.
