Doug, many/most people refer to themselves as Americans, because it is part of our country name. The United States of America. Just like my friends from Mexico refer to themselves as Mexicans due to using an abbreviated version of their country name, Estados Unidos Mexicanos, or States United of Mexico or in English order of words, it is the United States of Mexico.
Canada is a very old name, but it has officially been known by other names as well. John A Macdonald, later the first Prime Minister, wanted to name it the Kingdom of Canada and referred to it as such, in some of his writings. Then it was called, later, the Dominion of Canada, by some, and a number of other names, as the different provinces jointed together in a confederation of sorts.
So we and our northern and southern neighbors refer to ourselves by a shorter name in most cases. Our name is not directly related to being in North America, which you are correct about. But it is like the State of Rhode Island and Providence Plantations, but I have have never hear anyone from that state use the entire official name. They just say they are from Rhode Island. The Smallest state with the longest name.
Now when I am in Mexico with friends in Cuernavaca, they refer to where I am from as Estados Unidos or Oltra Lada (the other side) or just plain Gringo. LOL I did have a T shirt that said, when translated into English, I am not a gringo, I am a German. LOL they are much better liked by many in Mexico.
So there are many people that can call themselves North Americans, (Norte Americanos) not all can can use the shorter term of American for their country. May be some, I don't know what all the official names of all the countries of North America are in that country.
So depending on which side of the Rio Bravo del Norte, (the river we call the Rio Grande)I am on, is the deciding factor when someone asks me where I am from. So with the eleven (11) (counting Florida as one) Canadian Provinces and three Territories, most refer to themselves as Canadian, but not all the First Nation people do, from my personal experience. Just like in the US, some will first tell you they are Cherokee or some other tribe, then Americans. Same in Mexico, I once had a tour guide in the Yucatan area, when I spoke to him in Spanish, told me, he spoke English or Mayan, and asked which I preferred. Said he could speak Spanish but it left a bad taste in his mouth. LOL
We all have our issues, it seems.
joe b.
Stuart Florida
Formerly of Colorado and Alaska
2016 Fleetwood Flair 31 B Class A w/bunks
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