A healer is a Vulcan title for one who practices medicine on Vulcan, equivalent to an Earth doctor, although they are trained in treating animals as well. (TAS: "Yesteryear")
Senva, from the Vulcan Medical Institute, was a prominent healer, nominated for the Carrington Award in 2371. (DS9: "Prophet Motive")
This title apparently does not apply to all Vulcans who practice medicine, as Fer'at in ENT: "The Expanse" and the Vulcan doctors in ENT: "Stigma" used the title of Doctor.
Some Humans have also used the title of healer to describe a person who has medical training, often self-taught, but may not have the formal education of a doctor. Felisa Howard was a healer on Caldos colony until her death in 2370. Her granddaughter Beverly Crusher, while under the influence of the anaphasic lifeform called Ronin, temporarily resigned her Starfleet commission to follow in her grandmother's footsteps. (TNG: "Sub Rosa")
Doctor Julian Bashir also called himself a healer sometimes. (DS9: "The Passenger")