It has become a fashion for people in some places to “point out” that the USA is only part of America, and that “Canada is America too!” I would like to ask them to stop doing that.
I don’t think I know any Canadians who would say that Canada is part of America. Canada is part of North America – North America is Canada and the US and (if you include Central America) Mexico and so on down to Panama. South America is, well, South America. In total they are the Americas. But only the United States of America is simply America. Canadians are North Americans but not Americans.
That’s just plain and simple established usage. It’s so well established, I am reflexively offended when I hear someone say Canadians are Americans. (Canadians often complain about Americans. They don’t mean themselves.) It really doesn’t matter if your sense of logic tells you it should be otherwise; logic, as most people tend to think of it, has precious little to do with language use. North America can’t be shortened to America; would you call West Virginians Virginians?
So take it from a Canadian. Take it from as many Canadians as it takes. Canada is not America.