Why Wire Type Matters...
The most common types of pickup coil wire today are, 42 Heavy FormVar, 42 Plain Enamel, 42 Poly, and 43 Plain enamel and Poly. There are a few others too, but these are in your many of the most popular pickups that you are familiar with. What is the difference and why does it matter?
The number refers to the thickness of the wire. The larger the number, the thinner the wire.
Each of these wire types is insulated. Heavy FormVar adds about .0004" to the diameter. Plain enamel adds about .0002". Poly adds about .0006 to the diameter. This means that even with the same gauge of wire, the outside thickness is different based on the material.
Why it matters-
Inductance, the coils ability to store and transfer energy is basically a measure of its efficiency. The thickness of the wire and the insulation have a big effect on this.
Smaller gauges of wire have a higher resistance per foot. This makes it possible to have more of the total winding closer to the core of the pickup. This affects the overall efficiency of the coil.
The thickness of the insulation determines how closely together the wires sit. This has a big effect on inductance. The other factor is capacitance. The further apart the windings sit, the less high frequencies are lost. Insulation thickness also affects the efficiency of the coil by how far from the core the final windings end up. At the center of the pickup, the distance around the pickup is much shorter than at the end. This means that a large percentage of the "inductive capacity" of the wire is at the outside further from the core. We will discuss this more when we talk about coil shape.
So.... Wire matters. You can build two pickups with all variables being equal, and if the wire is different in either insulation type, or diameter... the ickup will sound different.