That's not a dumb question at all Airbass, but it is a little more complicated to answer than you might think.
A traditional P-bass pickup is a humbucker, meaning that the two halves of the pickup will cancel hum (noise) when working together. J-bass pickups, on the other hand, are single-coil pickups.
As a big generalization, humbuckers tend to sound a bit thicker, punchier and more low-mid heavy than single coils. Single coils will tend to have less punch and lower output and the sound will tend to be more 'open' and full-range sounding. These are, however, gross generalizations, and there are many other factors that contribute to the sound of an instrument including the rest of the electronic circuit, the scale length, the method of construction, string choice, etc...
To try to narrow down specific styles that are more appropriate for each type of pickup would be nearly impossible, as both J-basses and P-basses have been enormously popular for the past 50 years and have been used for playing countless different styles successfully.
The combination of a P&J has remained popular for a long time because it tends to give the player most of the benefits of playing both a P and a J bass, which are both very popular and versatile sounds.
Hope this helps.
E
