Kinda, sorta, but not quite.
Originally, “Doctor” was the European equivalent of “Sensei” or “Sifu”. It meant “teacher”; a doctor was someone who knew their subject well enough to not just do it, but also teach it. In order to claim the title, you undertook advanced study at a university, beyond what was necessary just to practice a profession.
The modern medical profession evolved from a few separate lines of study. There were physicians who studied ancient Roman and Greek medicine at the universities, and barber-surgeons who practiced applied surgery (to explain the barber thing: in the medieval era, if you need someone to amputate a limb, who do you go to for a really sharp knife?). There were also apothecaries (who developed into pharmacists), plus the herbalists and midwives amongst the peasantry.
Despite the fact that most of the physicians had only done the minimum professional training (i.e. Bachelor/Masters, not a doctorate), they began to call themselves “doctors” in an attempt to differentiate their educated status from the “ignorant empiricism” of the barber-surgeons and apothecaries.
However, as time went on, people started to realise that “ignorant empiricism” beat the crap out of classical bullshit (it wasn’t until the 20th century that going to a physician actually improved your chances of survival). So, the status of the barber-surgeons rose, while the status of the classically-trained physicians fell somewhat (but not as much as it should have).
So: physicians call themselves “doctors”, but most of them actually aren’t. And surgeons call themselves “mister” (historically; a bit more gender diversity now, thankfully) as a fuck-you to the snobbery and marketing bullshit of pre-modern physicians.
