Medicine is the science and practice of diagnosing and treating damage that affect the mind and/or body of living beings. It also deals with the prevention of diseases. The chief medical officer was usually responsible of all medical matters on a starship.
Klingon medical schools were considered to be worth attending only for traumatology or for orthopedics and thus these specialities were their best medical specialities. (Star Trek: The Stoneship Files: "Off Coverage")
Lyran Starfleet personnel was usually untrusting of Lyran medical practitioners; as such, most non-Lyrans in the Lyran Starfleet served in Starfleet Medical. (Star Trek: The Stoneship Files: "Highly Illogical")