P1= PIC
P2= SIC
This topic becomes confusing to US pilots because of the strange interpretation the FAA and the courts have created, one where conceivably you could have three guys in a Cessna 172, all of them considered to be Pilot-in-Command for different purposes.
Keep it simple. The PIC/P1 and SIC/P2 are designated as the operator-- in this case, the Captain (PIC/P1) and the First Officer (SIC/P2). Logging PIC time just because you may be the pilot flying or because legally you may have met the requirements to be PIC is questionable and risky (from a legal and integrity point of view).