FFF
I looked into this some time ago, and the best answer I could find was that FAA training is logged according to FAA rules, CAA/JAR training is logged according to JAR rules, etc. All this stuff can go into the same logbook.
I know people who log passenger hours, just for fun. It's not illegal (the logbook is yours to fill up with junk as you wish) so long as one does not add those hours in the totals.
I don't know what the FAA rules are.