its a little more complex than that, but thats still a good explanation.
on P-basses the pickups look like those stupid fucking staircase blocks in tetris that you can never use without fucking something else up. These are good for more vigorous playing like rock and metal etc...
the jazz pickups are a straight line, really narrow and have 2 magnets per string. These give a much more mellow and smooth tone, great for...well....jazz lol.
theres also pickups called "humbuckers" these are sort of a compromise, theyre alot more versatile in any field.

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