Dr. Leonard McCoy wearing the green-trimmed uniform of medical division, 2293
The medical department or medical division was a science department aboard the USS Enterprise incorporating doctors, nurses, and medics.
The red cross symbol worn by some in the medical division
After the M-113 creature infiltrated the Enterprise, Uhura declared a medical department alert, asking doctors and medics to acknowledge. (TOS: "The Man Trap")
After Leonard McCoy overdosed on cordrazine, captain Kirk lamented that the medical department knew as little as he did. (TOS: "The City on the Edge of Forever")
During certain time periods in Starfleet history, notably 2230s through 2250s, the mid 2270s, and late 2270s through 2350s, medical was its own division. and wore a uniform separate and distinct from the sciences division.
The precise structure of the medical department has never been clearly unestablished. In "Where No Man Has Gone Before", Mark Piper identified himself as the head of the "life sciences department", while in ("Operation -- Annihilate!") Kirk requested analysis by the "medical and life sciences departments", suggesting that they may be separate. In "Dagger of the Mind", Kirk hoped that someone in McCoy's department would have "psychiatric and penology experience".