Most of what Justa' said, with the exception of the capacitance on the scatter winding. Very tight overlaid windings have the highest interwinding capacitance - which exists in the theoretical realm, and cannot really be measured. As each turn is laid perfectly next to its predecessor, what might be termed "dielectric gap" is reduced. That is, you have only the coated insulation on the wire as the dielectric, and as the (insulated) wire touches its adjacent windings, the tendency is to create capacitor. Interestingly enough, in my daily work, I have to deal with "linear" capacitors, which are comprised of two wires, with fixed spacing run over very long distances (over a mile).
The old radiomen knew that there is more to a coil than it being a coil of a certain amount of Henries of inductance, which also could carry X amount of current and have Y amount of impedance.
What was discovered early on, was that the _shape_ of the coil matters. You can take a coil and wind it tall and skinny, or low and fat. The inductance, impedance, and wire gauge (for current carrying) are the same. What differs is a thing called "Q", for "quality factor". If you were building an RF filter, or audio filter, using a coil, you could adjust the width of the filter to a certain degree by adjusting the shape of the coil.
The shape of the coil comes into play with guitar pickups as well.
Justa's explaination of the P90 is incomplete. There are two magnets and steel poles that run down the center of the pickups (the screws), but this is sort of a means to an end. What those two magnets do, is to create a certain magnetic circuit which is both concentrated AND disbursed. That particular design makes a very tight field at the poles, but also creates a wide field surrounding the poles. A Strat or Tele pickup also has a tight field at the poles (which are themselves magnets) but they lack a great deal of that disbursed field. The "narrower" the field, the fewer added harmonics present. Strat and Tele pickups show this with their very tight and focused, brilliant top end. Taken another way, not only do humbuckers have to coils, but the magnetic circuit is also unique. There, you have two concentrated fields, with the disbursed field laying between the two. Lawrence found that he had to use VERY strong side magnets in his super humbucking design, which was created to add brilliance back into the humbucker. They were not small to make them fit in the existing space. That was a side benefit. They were small to keep the fields tight and add as little disbursement as possible. There is at least one Gibson / Lawrence design that uses no poles in the center of the coils, but a single magnet between the coils (like a rail, but not as we know it today). I cant remember which guitar or bass it was used on. It may have been the S1 or Ripper or one of those other "70's" oddballs they were making.
Another factor of coil shape is winding symmetry. Boutique winders will top load, or bottom load the coils - making the top or bottom fat, while the rest of the coil is tapered. This also has an effect on tone, and is part of the magic of the boutique winders recipe.
Basically... everything makes for a tone change. Wire gauge, insulation type and thickness, magnet type and strength, the magnetic circuit, the pole metal, coil shape... all of it and more.
