Good question, and a lot of so called westerns aren’t really Westerns. A lot of movies set in the Civil War are called Westerns, despite the fact that the setting is often east of the Mississippi. As in “Shenandoah”, for instance, or John Fords “The Horse Soldiers”. Some films have a Western aura, but aren’t set in the American West, or even in America at all. “The Man From Snowy River” is an example, set in Australia. And I don’t recall the title, but I saw one when I was a kid, about a British Police Officer in a small community in South Africa, who has to stand alone against a band of pistol packing, horse riding Boer frontiersmen. Not even set in the American West, but it had that aura about it. Plot was very similar to “High Noon”. I guess you could call it a genre, regardless of the setting. Kind of like what the French refer to as “Cinema Coloniale”, a genre usually glorifying colonialism and small bands of soldiers sanding off hordes of natives. The troops could be US Cavalry, French Legionnaires, or Scottish Highlanders, the setting could be the high Plains, Morocco, or India.