Be that as it may, the thing that sounds odd (and a bit arrogant) to most "outsiders" is using the name of a whole continent for a single country and its citizens. I (from Europe) would definitely consider a Canadian, Mexican or Columbian citizen as an "American" too, not only a citizen of the United States. BTW, I'm really curious what Trump thinks the "America" in his "Gulf of America" stands for - the whole continent or only the US?

Okay, maybe arrogant, but still, it's the only country in the continent to contain the word America, no?

Trump's definitely referring to the United States with his pointless renaming attempt because it's singular and not plural, but I'd be careful accusing him of thinking about anything. I doubt he does that very often.

I guess the Organization of American States exists. But usually it's pretty unambiguous which sense is being used; like, I guess you could call Mark Carney an American head of government but it's basically just being obtuse, unless it was in the context of, say, a meeting of Carney with other heads of government in the hemisphere, and then it'd be unambiguous what was meant.

Even "United States of America" is not unambiguous in the most pathological case; Mexico is also a country consisting of united states existing in the Americas.