All humbucking pickups work the same way. One coil is reverse phase and has reverse magnet polarity. This causes noise from each pickup to cancel out since the noise part of the signal from each coil has opposite peaks and troughs from the other.
The Split P pickup doesn't have two coils sensing one string but it's still humbucking. It's one coil per string but two coils total. One is RWRP with respect to the other, and that bucks the hum.
A jazz bass has two coils in a humbucking configuration. Notice when you have both pickups at full volume there is a mid scoop.
Two coils sensing the same string at different points can cause phase cancellation or loss of highs depending on how it's wired. This doesn't happen with a P pickup because there is one coil per string.
Also the Split coil retains a narrower aperture, or length of string it senses, as compared to a two coil per string design. Compare a Musicman humbucker width to one coil of a P pickup. Figure two coils together are sensing a wider area of string than one half of a P pickup.
A wider aperture means more mid content and typically a less crisp tone.
The Split P pickup is balancing several things at once to get the tone it has though. Notice one coil in a P pickup is wider than any Jazz bass pickup, but it's not as wide as a MusicMan humbucker made with two coils stacked side by side.
One other thing to note is that J bass pickups are wired in parallel, and the P coils are in series.