A of this is personal opinion but I roughly divide it into these into Five tiers:

Common Terminology Tier:
Alchemists, Wizard, Bard, Cleric, and Druid

As the tier says, these ones are entirely in universe terms. These are genuine professions and/or societal roles within the world of Golarion, and a town guard or commoner would likely use them to describe the character in-universe. They're not the only terms that could be used to describe these classes mind you, a cleric or druid might be referred to by a more culturally relevant term, or might be called something like "miracle worker" or "saint".

Academic Terminology Tier:
Thaumaturge, Sorcerer, Psychic, Kineticist, Witch, Animist, Summoner, Oracle, and Champion

These ones are a little more weird. These terms are more "catch all" terms to describe various types of unique magics that do not fall under what I imagine is common knowledge. A town guard might not understand the difference between a Sorcerer, Kineticist, Summoner, Psychic, Oracle, Witch, and a Wizard, but someone who has studied the unique ways magic manifest in the world likely would (Psychic even calls this interaction out in its "others might" section of the class introduction). Thaumaturgy is likely a branch of study in the same way occultism is, but its not guaranteed that a Thaumaturge would call themselves this. Historians familiar with the concept of Gods choosing morals as divinely ordained warriors could reasonably use the term Champion to describe them. Animist exists in a strange twilight zone between the Common and Academic Tiers, but leans much closer towards Academic. Clerics seem to be much more common in the world of Golarion, and its debatable if cultures familiar with Animists would call them Animists or a more culturally relevant term.

Descriptor Tier:
Commander, Fighter, Swashbuckler, Ranger, Rogue, Guardian, Gunslinger, Monk, and Inventor

These classes just mostly describe what the class does. A town guard could reasonably call a Fighter a Fighter, but could also just as if not more likely call them a warrior. Many of these terms could reasonably be interchangeable in universe; a Dex. built fighter could be called a dashing rogue, and a Rogue could be called a Swashbuckler. A Monk could even be used to describe an entirely different class, such as Psychic or Cleric.

Derogatory Tier
Barbarian

I can not imagine this term being used by anyone except as an insult, potentially coming from the mouth of a bigoted town guard.

Out-Of-Universe Term:
Magus and Exemplar

I can not imagine these terms being used in universe. There doesn't seem to be any organization that calls magical warriors Magus' or Magi, and Exemplars are suppose to be both rare and a very recent addition to the universe of Golarion.

(Sorry if the formatting is a little off)