I absolutely LOVE the sound of a good Jazzmaster and I've always thought the pickups in it were P90's, but Wikipedia tells me otherwise. So I turn to you guys, what is the difference between them?

I've had more experience with Jazzmaster pickups than I have with P90s. That being said, I believe the coils of Jazzmaster pickups are wider and shallower than those of P90s.

As far as actual materials go, I'm not sure what the differences would be.

The most obvious difference is the magnets: JAzzy's use alnico rod mags like a strat/tele, and P-90s use 2 bar magnets underneath driving the field up the screw poles like on a humbucker. This makes a pretty significant difference in tone. The rod magnets give you the fender "snap" which is direct and wonderful. The P-90 thing with screw poles is more blurred, warmer. Other than that the coils are somewhat similar (shallow & wide) but the wire type can change as well as the number of turns.

P-90's have way more output and are warmer/fatter sounding. Jazzmaster pups are more mid scooped and twangy.

imo

No one stated the obvious so I guess I have too...
P90s are Gibson.
Jazzmaster are Fender.

It should also be mentioned that the new and re-issue Fender Jazzmasters (US or import) don't have the original style p'ups in them - they're 'closer' to P-90's.
Lollar makes some good "real" JM p'ups.