The General Information Document I referred to yesterday is here:
GID44
As Noggin says, it is guidance but as the law doesn't specify how we record time I tend to accept official guidance
P1U/S can be used by a co-pilot performing the duties of PIC under supervision of pilot in command. Clearly that doesn't apply to many on this forum as we operate single crew aircraft.
The only other circumstance mentioned is that you should log PIC U/S for a successful flight test.
PU/T
Pilot under instruction for the purpose of gaining a licence or
rating,
or for conversion to an aircraft type within an aircraft rating group or class I suppose that
could cover differences training etc which does NOT lead to issue of a licence or rating.
Flameproof jacket on