See, Disco had it right. Doctors wore white, compared to the navy blue uniforms of all the other divisions, including Sciences. Presumably during the war someone decided that your medic being conspicuously covered in blood gave a bad impression, that was downgraded to nurses (SNW Chapel) and the doctors wore blue (although the slightly lighter shade than science divison). Then later, nurses got blue as well (TOS Chapel). Or was Chapel a full MD by then? Not sure about that.
In SNW Chapel is a civilian working on a starship because she's just that good or something, by TOS she's joined Starfleet.
