Citizens of the USA naturally refer to themselves as Americans and refer to the country as America.
When speaking to a person from Canada, he argued that it was incorrect to call the country America. Instead, I should be saying the United States (of America).
Is it incorrect to refer to the country as America? And even if it is, won't people from around the world understand that the USA = America?
I am a native citizen of the USA.
Is it incorrect to refer to the country as America?
It depends on context. Within the USA, it is generally understood that "America" refers to the USA (whereas "the Americas", for example, refers to the combined continents of North and South America). Note: This isn't really because of "narrow-mindedness" or anything like that, it's simply because, over time, it has become a norm in AE to use it as shorthand.
Outside of the USA, it depends on both where you are and the context of the conversation. For example, the use of "America" in other countries in the Americas may be offensive to some, or at least ambiguous. Outside of the Americas, probably not offensive (unless you are in a country closely tied to a country in the Americas), but certainly with the rare possibility of ambiguity.
And even if it is, won't people from around the world understand that the USA = America?
As mentioned above, it really depends. There is no global rule, and the interpretation will depend on where you are, what the common usage of "America" is in the country you are in, and the personal beliefs of whoever you are talking to.
If you are concerned or unsure, simply say "United States". While that is also technically ambiguous (there are other states that are united, actually the official name for Mexico translates to the "United Mexican States"; but for whatever reason it has become more commonly known as "Mexico"), it is commonly understood to mean the USA (even our government uses this shorthand globally, e.g. at the customs office you will see "United States Customs"), and it won't conflict with any other persons' use of "America". Additionally, within the USA, "United States" is commonly used and understood and won't raise any eyebrows or cause any confusion; it's a good global safe bet.
If you're really concerned, "USA" is 100% safe in and out of the country.
And, of course, within the USA, you can always say "America" without issue.
As Marcel Turing noted in the question comments, it isn't really an issue of "correctness" as much as it is an issue of common usage. Of course, in reality, it's slightly more complex, because while in an ideal world people wouldn't take offense at things other people innocently say, that isn't how it works. So you always need to at least be aware of local attitudes (and again, when in doubt, just go with "USA").
Personally, when I'm home I say "America", and when I'm travelling (even to e.g. Canada) I say "United States". This has never caused an issue (even in Mexico).
Edit: As for the demonym, as ntoskrnl points out in the question comments, "American" is the official one (but is shared with the continental demonym) and is usually understood, depending on the context, as referring to the country (with the same caveats as above; and unless the context is continents) with the only other real global option being "US Citizen". Wikipedia has a good article on Names for US Citizens. It also gives a nice overview of "American" in Demonyms: Cultural Problems.
The adjectival form has essentially the same issues, but without the "US Citizen" option.
ChrisW's answer gives a nice overview of context.
Please note this is all based mostly on personal experience, not so much canonical reference.
When speaking to a person from Canada, he argued that it was incorrect to call the country America. Instead, I should be saying the United States (of America).
IMO when a 'normal' Canadian says "American" in conversation they mean "from or of the USA", and explicitly mean "not Canadian".
As a Canadian I often don't use the word "America" to refer to the country: I'd say, "the U.S." as in "in the U.S. they do things differently", or "the States" as in "he emigrated to the States".
If someone in Europe talks about "America", I'd assume:
So for me (speaking as a Canadian) the word "America" mostly means "the U.S.A.": and I think most other English-speaking people agree.
If I want a word that includes Canadians or Canada and not just Americans/the U.S.A., I'd say 'North America', for example "NORAD was created to defend North America".
Perhaps your friend is technically/pedantically correct, but IMO their usage is unconventional.
While it is true that Spanish speakers refer to these ideas differently, this site's purview is "English Language and Usage". In the US and UK (and, I believe, Australia), if you say, "I've been living in America for 6 months", that indicates living in the US. Perhaps it's a misnomer, but that's the way the term has evolved. English, like most languages, is full of quirks like that. I have met Canadians who object to that use of the word America in principle, but I've never heard of a Canadian who would describe him/herself as an American; that's just not the meaning in English. They have a perfectly good demonym in the word "Canadian", and there isn't another demonym for Americans besides "American".
Also, how continents are viewed is different in different cultures. Some consider Europe and Asia to be one continent, and some consider Europe, Asia and Africa to be a single continent (as they are one contiguous land mass). To Americans and Canadians, North America is one continent, and South America is a neighboring continent. (This is also more accurate scientifically, as the two come from different parts of earlier land masses -- South America is more closely related to Africa, geologically speaking, than it is to North America.) So you would very rarely describe someone from Brazil or Argentina as an American in English. "South American" or "Latin American", yes, but just "American", no.
As a German, I can say that we also use "Amerika" to refer to the United States. While this is recognized by nearly all Europeans as being incorrect, they still use it for simplicity. Another term used especially in writing is "United States" (without America). If correctness is of the essence, we of course use "USA".
A term like "The Americas" by the way does not exist in German (also not in French if I'm not mistaken). There is really no other word for the combined North and South America than "Amerika".
Your Canadian friend is both correct and incorrect. He is a North American, not an American as it's understood by the majority of the world. The name of our shared continent is North America, not America.
The name for the combined landmasses of North and South America is the Americas. And, while you could in theory use the term American to describe anyone from those landmasses, most of the residents of the individual countries would take umbrage to that.
Most of the people across the world tend to identify primarily by their cultural groups. For some this represents national identities, some racial or ethnic identities, and for some this could be the continent, and in some cases all of the above. (e.g. Han Chinese vs Asian)
The usage of America and American for the USA dates back to the colonial period, prior to our revolutionary war. See here for more information.
The original name for the region was British America. This did, of course, include Canada. And, a resident of the region prior to the revolution would have declared themselves to be British.
It was not until after our revolutionary war, and the signing of the Articles of Confederation that the United States of America was founded. And, this was the point where the loyalties were divided and a new identity was forged. The Americans of the United States viewed themselves as a distinct new nationality. The Canadians remained loyal to the British Crown, and considered themselves British.
Looking at the construction of the name of our country, you will see America right in the name. The United States is actually a description of the structure of our country. We are the only country on the continent with America in its name.
America consists of 50 individual states, each of which functions with some degree of autonomy, under a greater federal framework.
So, in shortening our name to the United States, we are actually being ambiguous. In theory there could be other united states in the world. But, the United States of America makes it clear which country we are speaking of.
So, by convention, and by virtue of our right to call ourselves whatever we choose, we are Americans.
Referring to the United States (of America) as "America" might be an example of synedoche also.
A synecdoche is a figure of speech in which a term for a part of something refers to the whole of something, or vice-versa.
The Americas, or America also known as the New World, are the combined continental landmasses of North America and South America, in the Western Hemisphere.
Though it is debated whether it is a synedoche or not in some of the sources and some say that it is simply an abbreviation.
Also for the second part of the question:
Yes, America is understood as the United States of America globally also. It is simply another name and it is more convenient to use.
The people of a country are usually referred to by the geographic location in their country's name. We don't talk about Republicans from the Republic of France, we talk about the French. We don't talk about Unitedians or Kingdomians, we talk about the British or English*. We didn't talk about Unionists or Socialists or Republicans from the former/future USSR, we talked about Soviets (even though technically it's a government form, not a geography, it's the least generic term). So, people of the USA are Americans, not Unitedians or Statesians. There's no other X Y of America, so no ambiguity.
I'm not particularly well travelled or an expert, but, as a self-described American, IMHO American is a perfectly valid word for describing an inhabitant of the USA. The Google search for "American define" supports me in saying this (link here). For referring to an inhabitant of the continent of North America, I would use North American. For referring to someone in North America or South America, I would use "an inhabitant of the Americas" or something similar.
A person living in Canada is from America. The first map by Waldseemüller shows both continents referred to as America. I work with people in South America that simply say they are from America. It is very narrow-minded for the US to think they own the word because it is part of their country's name... and actually United States of America would signify they are on the continent of America. So yes our fellow Canadians live in America.
Just a great/funny site that I couldn't believe was out there.
