A medic was an individual trained in medicine who administered medical aid where needed. Doctors and nurses were examples of medics. Medics were not necessarily doctors or nurses, crewman such as Tom Paris who were properly trained in first aid or emergency medical procedures could presumably serve as medics.
In 2372, Ensign Carson attempted to summon a medic when Captain Benjamin Sisko was wounded in a battle with the Jem'Hadar aboard the USS Defiant. However, communications were down, so she had to retrieve the medic herself and bring him to the bridge. (DS9: "Starship Down")
An Alpha Hirogen medic and his Beta were present to monitor the health and mental activity of Voyager's crewmembers when the Hirogen took over the starship in 2374 and forced the crew to partake in dangerous holodeck simulations. (VOY: "The Killing Game", "The Killing Game, Part II")