I look at it like this:
Dual = instruction received, the instructor is PIC
PIC = any time you are the pic and sign the aircraft out
Copilot = any time in the RHS of a certified multi pilot aircraft.
caveat... I've never been a relief pilot, so don't know how that works.
Also it gets complicated in places that put inexperienced pilots into multi crew aircraft, as they don't have enough pic time to apply for the ATPL, so I've heard ways in which they justify logging pic time from the RHS.
One more complication, if flying in the RHS of a single crew certified aircraft, but as a proper part of a multi crew operation (e.g. B1900s are commonly flown with 2 pilots, but are single pilot certified)
I've flown as pic in half a dozen countries across 4 continents. I certainly feel your pain trying to convert from one system to another!