P1- you are the Captain and make all decisions you hold a valid licence and rating. You can also be P1 as a student on authorised solo flights.
P2- Only used on multi-pilot aeroplanes for which you need a type rating.
Dual - Any instruction given by an instructor
PICUS- only used on Integrated course of training for IFR flight
P1S- normally only used for tests that you pass or when operating as co-pilot. Not valid unless log book signed by the other pilot in command/examiner.
So if you are rewriting a log book there are only 2 of any use to you. P1 and Dual.