MarkerInbound,
How does the FAA FAR Part 1 definition of pilot in command influence the answer to the OP's question ?:
"Pilot in command means the person who:
(1) Has final authority and responsibility for the operation and safety of the flight;
(2) Has been designated as pilot in command before or during the flight; and
(3) Holds the appropriate category, class, and type rating, if appropriate, for the conduct of the flight."
I seem to remember some wrinkle about PIC "under supervision" maybe in Part 61 as related to logging time for licensing purposes ? But for the purposes of job hunting, I've seen some ads make the distinction that only FAR Part 1 PIC time was applicable.
Maybe not the same elsewhere in the world ? This is above my pay grade.