I have to admit I am a touch surprised at the length of and the discussion on this thread. Particularly the whole Captain/Co-Pilot/F/O thing.
I, in my innocence always assumed it was rather obvious. Any layman reading this or it seems some lesser experienced pilots may be a little confused.
This is my take on the whole Co-Pilot issue.
Airlines have a rank system, Captain, First Officer, Second Officer.
An aircraft may have a Pilot and and a Co-Pilot and even a third pilot. The Pilot is the Captain of the aircraft. That applies even to puddle jumpers like the Cessna 150. Even a student pilot is Captain when solo.
Terms like pilot flying and pilot not flying doesn't take away from the fact that only one of them can be the Captain/Pilot of the aircraft. When two four barred ranking Captains are on board one is the Captain/Pilot and the other is the Co-Pilot of the aircraft while both remain Captains in rank.
Confused????

No but suddenly I can see how some might be.