My point was that most of the class names are titles that members of those class may attribute to themselves. Yes, they might refer to themselves as something else (not every, or even the majority of fighters, might think of themselves as a "fighter"), but, for the most part, they wouldn't deny that title.
Barbarians are an exception, however. As you said, many people are called barbarian, but usually by their foes. In your examples, the Norsemen, Moors, Europeans, and others would not call *themselves* barbarians, even if they happened to use a fighting style that would be easiest to mimic in D&D with the barbarian class. Its one of the few classes where I don't really picture any barbarian claiming to be a barbarian, just because of the usual connotations behind the word.