It’s pretty common to refer to the United States of America as simply America, or anyone or anything from the country as American. This however, can be somewhat controversial.
The term America was coined by Martin Waldseemüller in tribute to Italian explorer Amerigo Vespucci, who mapped the east coast of South America and the Caribbean in the early 16th century. At the time, it was used to refer to the whole of the New World, what we now refer to as the Americas.
However, with British colonisation of North America, the term America in English came increasingly to refer just to these colonies, which has been retained to this day in how we refer to the United States.
Understandably, people from other countries in the Americas can feel aggrieved at not getting to be referred to as Americans, at least not without a hyphen. Understandably, it’s an unfortunate consequence of the global dominance of the English language that the most populous English-speaking country gets to lay claim to the words that could easily be used to refer to anyone from the Americas.
Even the fact that we say the Americas is an example of this. Logically, there’s no reason we can’t refer to North, South, and Central America together as America. There are no politic definitions of continents: rather a continent is defined as a continuous expanse of land. Strictly then, you could say that even though North and South America are separated by the narrow isthmus of Central America, the whole body is still one continuous expanse, and could be referred to as simply America.
But of course that would be confusing, as America has become so synonymous with the United States. And even though someone from Canada or Argentina is perfectly entitled to refer to themselves as American, that would also be confusing, and inaccurate in the case of an official form, for example.
Sadly, there isn’t much we can do to change things. Let’s imagine we decided to do so, officially. Trying to get people to refer to the United States simply by that name wouldn’t be so hard, but what adjective could replace American? Columbian has in the past been used as a literary adjective to refer to the United States, but obviously that would just make things more confusing. And I don’t think many people want to maintain the association between Christopher Colombus and the United States. There aren’t many other obvious choices, as multi-word names of countries don’t lend themselves easily to adjectives (see Moe’s predicament above).
And how easy would it be to get used to America referring to the continent(s) and not the country, and to meet someone from another country referring to themselves as American? It’s hard to enforce changes in any language, but particularly one so widely-used and flexible as English. The words we use are largely determined by how many people use them, and considering that all English speakers use America and American to refer to the United States, that’s not really going to change any time soon I’m afraid.