The use of "American" to designate residents of the United States dates back to a time when there were no other countries on the continent. If you lived on the American continent in the 1700s, you were either Indian, or an English, French, or Spanish colonist (or a slave). In the 1770s, 13 of these colonies rebelled and formed their own union. It wasn't really a country though, since each had its own money, laws, and government. To differentiate them from colonial citizens, Europeans called them Americans. Most Americans thought of themselves as citizens of their state (Virginians, New Yorkers, etc.), and in fact it wasn't until after the Civil War that they began referring to the United States as a singular entity, rather than a plural.
Your description of America as a single continent with "plenty of different countries" betrays a very Afro-Eurasia-centric view of the western hemisphere. Unless you can point out Wisonson on a map, or tell me what the Federal Republic of Central America was, maybe keep your eastern hemisphere judgements to yourself.
That description of American Colonists is exactly why there was a rebellion.
The English treated the colonists like second-class citizens, going so far as to try to get Ben Franklin to answer for things like the Tea Party, while he was in England, and a Loyalist.
The simplistic "rebelled over taxation" is just a representation of how the Crown and European Brits viewed and treated the colonists.
Colonists didn't quit Britain, the Briton's quit on the Colonists.
I've worked with folks from around the world (including Central and South Americans), some can be touchy about it.
Had to tell them "sorry, I, as an American, don't define these terms. Blame Europeans, not me".
"US", "America", "Americans" all have specific denotations... per EMEA, and hell, even Canadians.
It's like nicknames - if you have one, you didn't choose it. It was earned or applied by someone else.
Yeah... I learned Spanish in Mexico as a wee lad, the folk living North of there were called "Gringos" or "Yankees". Back in Europe, behind the iron curtain, it was "Americaniard" or "Yank", rarely "American"... even when people meant no disrespect.
Then in Spain... (@[email protected], you may want to see this)... "American" refers to any citizen of the whole continent... even the official dictionary itself, in it's latest update, actually states:
debe evitarse el empleo de americano para referirse exclusivamente a los habitantes de los Estados Unidos, uso abusivo que se explica por el hecho de que los estadounidenses utilizan a menudo el nombre abreviado América (en inglés, sin tilde) para referirse a su país. No debe olvidarse que América es el nombre de todo el continente y son americanos todos los que lo habitan.
The use of American to refer exclusively to the inhabitants of the United States should be avoided, an abusive use that is explained by the fact that Americans often use the abbreviated name America (in English, without accent) to refer to their country. It should not be forgotten that America is the name of the entire continent and all those who inhabit it are Americans.
So yeah, kind of like nicknames... but then some places have different rules about the nicknames. 😉
(...and then there are the actually vulgar despective nicknames, which I won't get into here)
There weren't many Indians on the American continent in the 1700s. They were busy getting oppressed by other British colonists back in India at that time.