One important thing about historical European medicine is how ridiculously classist it was for a long time, one major example being how much pushback germ theory got because the doctors of the time were apoplectic at the suggestion that a gentleman's hands could be unclean. In the time period of the quest, it's largely divided into Physicians and Barber-Surgeons. Physicians are Noble Men Of Science who study a heady mix of science, mysticism, and nonsense, and charge often outrageous fees for their services, which is usually limited to diagnostics and medicines as actually taking up a blade and doing stuff to a living body as seen by many of them as gauche commoner work (though taking a blade to a dead body is the study of anatomy and perfectly acceptable as long as the local Morrites don't catch you doing it). Barber-Surgeons aren't quite as grimdark as they sound - being a decent barber requires sharp blades, a steady hand, clean premises, and decent people skills, so if surgery needs to be done they're a natural fit, and they tend to be more reasonable with their fees because they depend more on repeat business than Physicians. Both are heavily regulated by their respective Guilds, and performing either without a license is legally considered assault.
To boil it right down, Physicians add things to a body and call it medicine (an old meaning for the word 'physic' is medicine), while Barber-Surgeons take things away from a body and call it surgery.