Its true that most of the world may refer to football played in North America as American football, but the proper way to refer generically to both games is Gridiron football.
Exactly. Canadians invented a form of Rugby, the Americans took it and quite rapidly changed it, and with the introduction of import players, coaches and executives, the Canadians changed their game to closely resemble the American one, which continues to this day. So to say they are playing our game is correct. But so is saying we are playing theirs.
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