+1. To expand on this point, this is different in English vs. Spanish, which is where a lot of confusion comes from.
In English, America is always the United States, and the Americas is always the continents. American always means United States-ian. There is no word for "someone from anywhere in the Americas".
https://en.wikipedia.org/wiki/America https://en.wikipedia.org/wiki/The%20Americas
In Spanish, traditionally, America is the continents, and Las Americas is nothing. Americano traditionally means "someone from anywhere in the Americas".
However, because of the influence of English, people sometimes use Las Americas to refer to the continents and Americano to refer to United States-ians. So it's a little more complicated in Spanish.
https://es.wikipedia.org/wiki/Am%C3%A9rica https://es.wikipedia.org/wiki/Las_Am%C3%A9ricas https://es.wikipedia.org/wiki/Americano_(palabra)
You're conflating America with the Americas.
The Americas is the collective name of the continents.
America is just shorthand for the United States of America.
Just like Mexico is shorthand for its official name, the United Mexican States.
And there's no confusion because there's basically never any situation where somebody wants to refer themselves as an inhabitant of the Americas, the same way nobody calls themselves Eurasian. It's too large an area to be useful. It's two continents (in most cultures). Geographically at the largest scale, people tend to refer to themselves as North Americans, South Americans, Latin Americans, and so forth.