I've posted something similar before, but yeah a charcter's class and their identity may or may not line up. A wizard could call themselves a wizard, but they could also call themself a Magus, a druid might call themself a Witch, a sorcerer and Enchanter, so and and so on.

In other cases a character probably DOESN'T call themselves their class. A probably refers to themself as knight, warrior, soldier, and a lot of other classes would be similar. Some are both too, where a ranger (class) might be a ranger (profession), but a rogue could have that job as well and refer to themself accordingly. A cleric or druid in class might call themself a monk because that's what they are in the religious hierarchy, anyone on a ship might call themselves as a sailor, the entire party could accurately just describe themselves as adventurers, etc.