Military Q:
Back in WWII I believe many USAAC/USAAF crews mostly stayed with their individual aircraft. So in some sense they owned it; painted their wife/GF’'s name(s) on it, marked down kills, etc.
That’s not common US practice since much after WWII.
What was done with tactical aircraft in my era and seems to still be done is they paint the name of *a *pilot on the canopy rail of *an *aircraft. Likewise they paint the name of the “crew chief” (main maintenance guy/gal) on the other side. Two crew aircraft (e.g. F-15E) will also have the name of the back seat weapons dude(tte) painted abeam his(her) seat. (I forget the fancy new name for that role; it was WSO (and exclusively male) in my era.)
The maintenance guy/gal does “own” the aircraft in some sense. He/She works on that same airplane every day getting it ready for each mission. When it goes into the hangar for more significant work, he/she accompanies it there and helps the dedicated hangar workers do their thing to it. OTOH, if the airplane is shipped off-base the crew chief is assigned another aircraft or other maintenance duties until assigned to another aircraft.
By contrast, the pilot has no particular connection to “his” airplane. Any pilot will fly any airplane on any given day. In my era we had about 2x as many pilots as aircraft and so not everyone could have their name on an aircraft at once. The brass all had their name on one permanently, so the ordinary guys had to share naming on the few remaining airplanes. They typically got their name on a plane for only a few months out of a typical 2-3 year tour. Getting your picture taken on the ladder standing by your name on “your” airplane was an important part of the ceremony.
In my era a pilot with his name on a jet was encouraged to take an interest in it, foster a relationship with the crew chief, and be a “dutch uncle” to the beast. This was mostly in service of the idea of promoting maintenance vs. ops cooperation and a feeling of shared mission. Which didn’t really work very well. Most pilots didn’t want to be bothered and over time ops and maintenance generally had a mildly adversary relationship, just like sales and production in a corporation. Each side achieving its individual goals implied some imposition on the other side which interfered with them achieving their goals. Smart leader-managers made sure that each side was judged on the collective results. Dumb stove-piped manager-leaders did not; managing instead by individual unit statistics.
Airlines Q:
Captain and co-pilot are separate and non-interchangeable jobs. Any given pilot is one or the other; never both. In most cases the Captain is senior in the company / employee / union member sense of the word. All pilots start out as co-pilots and, once their company / employee / union seniority permits, have the opportunity to “upgrade” to Captain. Most do; some don’t. And some never have the opportunity due to mergers, layoffs, shrinking employers, other earlier careers, etc.
A scheduled unit of work, commonly a called “trip”, is one or more consecutive workdays with one or more flights per workday all grouped together. A single Captain and a single Co-pilot will be assigned to work that trip together as a team. Long-haul oceanic flying may need a second or third co-pilot and/or in some cases a second Captain as well. If so each position will be filled by an appropriate worker.
The Captain is always in charge. On multi-Captain long haul, one Captain slot is pre-designated as the primary slot. Whoever was assigned that slot is in charge for the whole trip.
Whenever we’re flying, one pilot is the so-called “pilot flying” = PF. He/she manipulates the controls and acts in charge of the operation on a moment to moment basis. Like the “officer of the deck” on a ship. The other pilot fills a role called “pilot monitoring” = PM. He/she talks on the radio, does administrative tasks, and watches and double-checks everything the PF (and the aircraft) does. The PM mentally simulates being the PF at every step of the way.
And, just like on a ship, if something significantly out of the ordinary happens while the co-pilot is acting as PF it’d be common for the Captain to eventually have a “change of control” and take over the PF role once the immediate action crisis is passed and we’re dealing with the consequences.
PM is in no sense an apprentice role, but you can see it affords a lot of opportunity to learn by watching and almost doing without the strain of being fully engaged in driving the beast.
On a typical two-pilot trip, the Captain and co-pilot will alternate taking the PF & PM roles on each flight. There are other considerations, but the general goal is to fly each role on about half the shared flights.
The flights with more than two pilots always have one active PF, one active PM, and the other(s) are resting (trying to sleep in the cabin) awaiting their turn in the driver’s seats.
Bonus nugget:
For those airlines which operate more than one aircraft type, generally speaking each pilot is qualified to fly just one type. That type can change over the years as careers progress and the airline renews the fleet with new types to replace obsolete types. Some folks get on a newly bought type early in their career and stick with it for a whole career; others prefer to hop around to different types every few years.
The military is similar in that pilots are generally qualified on only one type at any given moment. The dynamics of when and why they change types are different. Turnover of personal is faster, but turnover of new types is slower. The military also has the factor of tours spent in non-flying desk jobs, at the training command teaching new pilots, etc. Plus ever-increasing rank. Features the airlines mostly lack.