An 'American' is a vague nationality noun. It pretty much refers to people from Patagonia Argentina up to Canada. It’s like asking a Chinese what nationality he is and he answers, I’m Asian.
U.S American is less vague but if you really want to be anal about it it's still not specific enough. Mexico official name is "United States of Mexico" or "United Mexican States" according to cia fact...

The sailor does not pray for wind, he learns to sail. --Lindborg