“Barbarian” is just a class name. In context if DnD it’s a warrior who enters into an enraged, frenzied, maniacal state during combat. He can be a noble from BG, he can be a Halfling from the village, or a wildling from the mountains. There is no discipline to their combat, just pure fury and anger.

Barbarians from northern tribes (wolf, elk, bear etc.) are predominantly “Barbarians” by class, but they can also be rangers, priests, fighters, sorcerers etc.