Just want to pipe in with a little bit about smaller vessels. I can’t say anything with authority about the military, only what I have seen on a research vessel. On the vessel I was on, there were three officers - a captain and two mates. All three stood their own watches (4 hours in every 12 hours). During a watch, they were “the man in the hot seat,” so to speak. That is, the officer on watch ran the ship, was responsible for maintaining course (or position), keeping tabs on what was happening on deck, and, if the shit had hit the fan, would have been the one to organize emergency responses.
Outside of watch duties, there was some sort of distribution of tasks that I am less familiar with. From speaking a little bit with the officers (great guys, all), I have some semblance of an idea, but I am afraid that specifics are getting confused with speaking with my brother-in-law, who is a mate working for Exxon/Mobil. However, something like the following is probably not too far from the truth.
Second Mate: Review of Ship-board Equipment, inspections, ensures crew (and science crew) are familiar with emergency routines, etc. Possibly oversees stocking of consumables.
First (or Chief) Mate: Plots course(s), runs drills with crew, handles personnel paperwork and issues.
Captain: Reviews actions and decisions of mates, bosun (guy in charge of storage and/or deck operations), chief engineer (guy that makes sure the boat goes), and other department heads (e.g. a chief scientist - but that gets really confusing really quickly).
Regardless of my flawed memory, I think the basic point, as has been mentioned, is that the captain of a vessel not in battle is there to be the QA guy, make sure stuff gets done, and is the final authority. May or may not stand watch as often as the mates, but only gets to sit in the “easy chair” when all is going 100% right, and then only for a short time before he has to go out and check to make sure things are really going 100% right.