All the terms refer to different parts of the job.
PIC vs CoPilot is who is legally responsible for the aircraft PIC is the one who must ensure the legality of operations. CoPilots are any other pilot on board assigned to operate the flight, but not finally responsible for it.
Captain vs FO/SO and so on are payrole and company specific titles usually with a list of responsibilities associated with compliance and company directives. You can have two Captains on a flight but only one will be assigned PIC, the other as CoPilot.
PF/PM/LP/RP are operational duties. Procedures will be specific to operating said position in flight. Usually a combination of manufacturer and operators procedures to ensure compliance and safety of flight. Anyone appropriately trained can perform each duty, PIC does not have to occupy the LP position, however that is the norm.