Mmmm...jamestkirk...If you are converting from type to type, surely it has to be PI/S, I've done a google to find out what to log for what, and couldn't find anything conclusive, I've looked on the CAA site, gave up in the end! Back, after my training, when converting to type, I was always told to book it as PI/S.
And you were told incorrectly by an Instructor who clearly had no idea what they were talking about. The regulations on when P1/s is used in SINGLE PILOT aircraft are VERY clear. A checkout with an Instructor is not P1/S. It is either P1 or PUT nothing else.
It is also not a JAR thing, it was also an old CAA thing.....
Opening a new can of worms is the times when someone should be P1 and therefore the Instructor logs nothing. If converting between types in a class it is training and the Instructor is P1. If I am just running someone around the circuit a couple of times for club or syndicate 28 day rules then I log nothing as I am not there teaching. Other Instructors may insist they are P1 all the time, it is there prerogative. Personally I gave up caring about the hours long ago.