We could get into some electrical theroy but that would get difficult. Some may think that by merely putting X amount of winds and achieving X amount of resistance that you get a certian sound. That is just not how it works. Every variable plays a part to creating a certian sound.
The best overall view of where the characteristics come from would be coil shape, height versus width, magnet material, ceramic, alnico 2,3, 4, 5, wire gauge, and how tight or loose the coil is wrapped. Height and width contribute a lot. In general terms the taller the coil, the more "sparkly" and cleaner the sound. The fatter the coil the sound gets a little warmer. Magnet material also contributes. Alnico 5 is brighter than its lower number counter parts. This is due to the alloy of the magnet material. An alnico 2 will have characteristics more like an aged alnico 5. Alnico 2,3,and 4 tend to be a bit smoother with a little less output. The tension of the coil will change the capacitance and inductance and will also lend to the character of the sound. The guage of the wire will change the sound as well. The tele neck pickup is wound with a smaller guage which is one of the reasons its a little smaller than its bridge and its strat counterparts.
There are other variables as well. The wood, pickup placement, string length also come into play. So if I had to say what creates the sig sound it would mostly be the shape and size of the coil, the mags, and winding techniques followed by the woods and construction of the guitar.
