Please compare/contrast P-Bass & J-Bass...

... pickups. I'm curious as to how the P-Bass pickup acts as a noise cancelling unit when the coils only cover two strings each. I thought that the separate coils on a full humbucking pickup going in opposite directions were what cancelled the noise. Does the split coil work the same way despite the fact that the coils are really only picking up two strings each? I read Leo's rationale behind using two polepieces per string with the second Precision pickup and the Jazz pickup, having to do with softening the attack. Would someone please explain why the latter Precision and the standard Jazz pickups sound so different. Thanks.