The correct demonym for the U.S. in English is "American".
In Spanish it's 'estadounidense' which is cool, but there's no equivalent in English. Anybody who actually cares about the ambiguity of the U.S. demonym probably has too much time on their hands.
So these are people who live outside of the United States that describe their nationality as "American"? Do any of them live in countries that actually have "America" in the name?
Btw. I'm european, even though I don't live in a country that's even part of the EU (we are part of both the EEA and Schengen area, though)...Norway FTW.
But then South Korea simply calls itself Korea and ignores the north.