In a single pilot aeroplane such as the PA28 there are only three operating capacities that may be claimed for licensing purposes, PIC, Dual or SPIC. Dual (as defined in FCL.010) may be claimed only if receiving flight instruction from a properly authorised instructor and SPIC is reserved for students on an approved integrated course. In the circumstances described by the OP, therefore, one of the pilots may claim PIC while the other is simply a passenger - these roles may, of course, be exchanged during the flight but the sum of the PIC time claimed by the two pilots may not exceed the total flight time. The only other operating capacity recognised by the UK (but not by EASA) is SNY (supernumerary) although it counts for nothing in licensing terms.
A pilot may record anything (s)he wishes in his/her personal logbook but, when applying for licences, ratings or certificates, may claim only flight time gained in accordance with the regulations. Any flight time gained in SEP aeroplanes and recorded in a logbook as P2 will be ignored for licensing purposes by the competent authority.