It's difficult to explain quickly but I will try.
I wind around the magnet and format.
Certain winds for certain magnets within the type of pickup. This is important most with Humbucker guitar pickups. Some neck pickups are muddy , because they are actually overwound for that position. One thing I do for some Humbucker models is wind to a PAF reading , but with #43 wire. Les turns , same ohm reading. Beautiful sounding neck and the reading is what is stuck in a lot of people's head. My Archangel set for metal guys is like this. Neck is 8.6k , but wound with #43. Bridge is 16k , #44 with A5/C8 magnets. The neck does clean melodic intros perfectly with articulate well defined chords while keeping the highs. Great for fast playing and no mud. For the Bridge high gauss levels and both sides of each coil being charged really helps with big chords and also quick to respond to fast playing.
With single coils you get one shot. So it's about size of wire , number of turns and the pattern or crossover of each layer. Known as TPL or turns per layer. The TPL is kind of like capacitance. If the coil has a low TPL count it can handle chords. If wound like a garden hose or a doorbell the coil it can become brittle or shrill sounding depending on how it's used.
For bass pickups I always go with a LOW turn per layer count to make sure the lows are fat even and do not break up. With a Strat coil you have to find the sweet spot in one shot. Good lows while keeping the highs. If too many turns the pickup becomes darker. But again it depends on the magnet. A5 or ceramic can have a lot of highs , so these magnets are usually found in high wind applications. Then there is what's called the BH curve. This effects overall frequency. Builders that understand this usually try to have a metal free (except blade or Pole piece) pickup like the Bill Lawrence SF / Slant /Dimebag pickups. Also assemblers like DiMarzio will use ceramic magnets then use brass to pull down the BH curve and mimic a Alnico frequency (not saying they sound like Alnico). I do not care for the ceramic / brass thing but plenty of people like what it does and tons of albums have been recorded with this arrangement. Van Halen 1 and many metal albums to name a couple. At 916 when trying to maintain all the frequency. We cut vulcanex baseplates for Humbuckers and no covers. Some players figured this out not knowing exactly why , some on accident. Les Paul pulled his covers off. Somehow he knew , Jimmy page had his covered PAF neck and open T Top bridge in his LP#2 (We offer replicas).
With bass pickups , you want fat well defined bass. Gauss is very important. This is why you see a lot of large Ceramic in bass pickups. One of the reasons the SF stuff is so liked is the quick punch single coil backed with all the gauss that could be provided in that time period. Today , Neodymium is available and what I use whenever the customer allows. Way to many are shy about Neodymium and stick within the old box of A5 in coil , ceramic or a battery powered Operational Amplifier. Due to my HiFi background and understanding of op amps. Any op amp that can run on 9v is not going to be something great. (Sorry Active Players). My recommendation for getting away from batteries/op amps is Neodymium. Neo will punch your bass preamp in the face. Not one bass player that's ditched the battery for 916 neos has moved away from neos yet. As everyone here knows bass pickups can be as low as 4 ohms , but that requires big ceramic/gauss , all the way to Duncan 19k+ Alnico 5 in coil trying to wind their way to more output. (Squeezing the preamp) . My theory regardless of designs is the less vs more wire , more magnet than less unless it's for vintage tones in guitar where magnets like Alnico 3 that barely have enough cohesion to stick to metal sound beautiful. A3 is one of my favorite P90 magnets and is also great in Humbucker. A3 is a perfect pairing with old Fender amp circuits / 6L6 , like A2 is great with Marshall circuits / EL34.
Sorry about rambling , but this is like trying to talk about engine cam shaft profiles. Huge can of worms. Any questions feel free to ask.