No.. I'm not confused... I know that the common way is to call US citizens for Americans. But I still think it's wrong. I can't think of any other case where you call a habitant of a certain country for the name of the continent AND there's other countries on that continent (eg. you call Australian for their continent name.... but then again.. there is no other countries on that continent).
I take the other point of view on this issue. I'll explain why.
Although its official name has changed, at one time Brazil's official name was Los Estados Unidos do Brazil. The United States of Brazil. Canada is The Dominion of Canada. West Germany was the Bundesrepublik Deuchtsland, the Federal Republic of Germany.
Thus, following that pattern, a name like The United States of America would seem to imply that the country is America, and it happens to be a United States; that's its form of government. (It's also a Republic, of course, but there's no reason why two terms can't apply to its form of government.)
It can be called "The United States", just as Canadians once occasionally referred to their country as "The Dominion" in some contexts, or as Americans will sometimes call their country "The Republic", as in a sentence like "Corruption in government is a threat to the well-being of the Republic". This, however, is synecdoche: the name of a part (or, in this case, an attribute or quality) is used as the name of the whole. (Synecdoche is said to be a case of metonymy; however, in metonymy, the name of the whole is used as the name of a part or a quality, so it would seem that synecdoche is metonymy in reverse. However, I may not be understanding the references I hastily consulted, not being well enough acquainted with the classical figures of speech.)
But what about the fact that South America isn't part of the U.S.A.?
North, South, and Central America, in English, are known as "The Americas", and
never as America. (In some of the Romance languages, such as French and Spanish, however, this is not true, so in those languages there is an issue.)
Still, this part of the world is called the Americas because of a map by Amerigo Vespucci.
There are other names for it as well.
For example, the television network CBS is called the Columbia Broadcasting System. Because the United States is part of the New World, which became known to Western Civilization as a result of the voyage of Christopher Columbus.
With the possible exception of Quebec, all of Canada is British, and Guyana and Jamaica and the Turks and Caicos Islands are other present or former British colonies still within the Commonwealth.
Yet, one Canadian province calls itself British Columbia, and no one objects that this is unfair to Jamaicans or Ontarians.
And, of course, there is the República de Colombia.
If we're going to object to the United States being America, because that name includes three continents, doesn't exactly the same objection apply to Colombia? Aren't they unfairly stealing our name?
No. The United States of America is America, just as the United Kingdom of Great Britain and Northern Ireland is Great Britain and Northern Ireland, and the République Française is France. And people will just have to deal with it.