Physician in its different senses can be used to describe any of the three strands, so patients are cautioned to use the word advisedly and make sure they know exactly what they are hiring.
Shade's magical healers work through a trance state, which gives them a unique perspective on the patient's body and allows them to detect and affect things imperceptible to the normal senses.
This state is called the 'Quigley trance' in central Terrimoire and the 'Laroche state' in the deep southeast.
However, it must be understood that magical healing is not a replacement for non-magical methods. Broken bones need to be set, open wounds cleaned and protected and patients calmed before messing about with trances. Healers are not generally mystical or afraid of getting their hands bloody.
The healing trance is in large part a diagnostic technique. Its practical applications for a beginning healer include accelerating natural healing and clearing infections. Experienced healers may be able to cure a virus and do more exciting things.
The same techniques, if used maliciously or incompetently, can cause a great deal of damage.
Magical healing can't raise the dead or alter genetics.
Some details of healer training, procedure and values are mentioned in Hex and in comments made by Siri elsewhere.
Student healers, after training with a mistress or master, spend some time on the road, a journey that is called a tournée across most of Timoire. A touring healer works for food and board on principle; this, according to Siri, is to provide healthcare for communities too poor to pay. In places with incumbent healers of their own, the student generally stays with them for a short time and helps out with their housework and patients while learning.
It seems there are complicated healer rules concerning patients met while travelling. These are often helped for free.
The Twine Wars period is a time when unmagical sawbones are beginning to change into competent doctors.
Dual-field healer-doctors, and communication between the two strands, subsequently become widespread. There is a general threshing of good science from superstition.
Genetic therapies (and post-fertilisation screening/engineering) begin to be developed in future.