I know there are variations that are derived from the three main types of pick-up mentioned. Generally speaking though, am I right to think of it this way?
P means a split coil humbucking pick up,
J means a single coil pick up
MM means a twin coil humbucking pick up.
I voted MM MM because of the five basses that I own, four have pairs of humbuckers. The fifth, a fretless, has a P/J set. I'm not that particular. I'll work with what I've got.