Ah - that's slightly different. If you're in a private owner group, any new group member isn't 'hiring' an aeroplane from you, they are effectively becoming part owners. So in your case, if they've flown that particular breed of aeroplane before and are just familiarising themselves with your particular one, then indeed no 'training' is taking place. Thus one pilot will be the Commander and will log the whole flight time as such, the other may log P1 time (not in this case P1U/S) only for the actual time he/she is at the controls but must annotate 'Shared' in the Remarks column and the actual Commander (who does not need to be a FI or FE) must countersign the entry.
For example, say a fellow pilot invited me to fly with him in his aeroplane of a type with which I was familiar and offered me the take-off and half of the flying on a 2hr trip. He would log 2hr as Commander (P1C), I would log 1hr P1 with his name as Pilot in Command, he would countersign my logbook entry.