When you're non-commissioned, as McCoy may be, does that make them essentially draftees?
Doctors/surgeons are not, nor have they ever been
non-commissioned officers (petty officers and chief petty officers in naval teams). They started out as
warrant officers (which sit between NCOs and commissioned officers) and eventually migrated to "staff commissioned officer" status, which arguably has as much in common with the US commissioned chief warrant officer as it does regular commissioned officer status.
Rand was a yeoman which is a noncommissioned officer. In the current U.S. Navy, yeoman start as a E-4 and can advance to E-7. 2024 Pay chart:
Technically, E1s to E3s can also be rated, but I'd certainly agree as far as
independent duty rated personnel including yeomen.
Note: From Charlie X, Tina Lawton was Yeoman Third Class, probably an E4.
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YMN3 Lawton is a bit of an odd-duck as while a variety of different grades of enlisted have been mentioned or implied at various points, but she's the only person who has even been given a grade equivalent to Petty Officer Third Class:
ENT: Crewman (no insignia), Crewman Third Class (one stripe), Crewman Second Class (two stripes), Crewman First Class (three stripes, acts as Officer of the Watch). More senior NCO grades may exist.
TOS/M: Crewman (no insignia), Able Crewman (MMs only), Petty Officer Second Class (MMs only), Petty Officer/PO First Class, Chief Petty Officer, Senior Chief Petty Officer (MMs only), Master Chief Petty Officer (MMs only).
TNG: Crewman (no insignia), Crewman First Class (no insignia on 2360s uniform, may wear a single chevron on 2370s+ uniforms), Petty Officer (might wear a single black pip on the 2360s uniforms, may wear two or three chevrons on 2370s+ uniforms depending on seniority), Chief Petty Officer (single black pip on the the 2360s uniforms, may wear three chevrons and a pip on 2370s+ uniforms), Senior Chief Petty Officer (single black pip on the the 2360s uniforms, may wear three chevrons and two pips on 2370s+ uniforms), Master Chief Petty Officer (single black pip on the the 2360s uniforms, may wear three chevrons and two pips on 2370s+ uniforms).
Rand may have been a E-6 since she serves on the staff of a general officer (i.e. Captain of a capital ship).
General or flag officers are generals, admirals and sometimes commodores and brigadiers at O7 and above, commanding officers -- even of capital ships -- are senior officers (allegedly universally O6 in Starfleet, but more plausibly ranging from at least O4 to O6 depending on ship size and mission parameters).