America and the United States are generally used interchangeably even though technically not identical. They are more like apples and oranges.
The United States is defined in the Texas statutes as a political subdivision, which is an artificial thing.
America is a geographical location, or a concrete object.
(sigh) Sometimes I wish I were more articulate so I could explain my position better!
None of that will stop the vast majority of people from referring to the United States as America or its citizens from being called American citizens.
It is as useless as trying to explain the difference between envy and jealousy. But you can keep trying.
All those illegal aliens can say Hey we are all Americans amigo. North Americans.