Magnet wire
Magnet wire is a tiny insulated copper conductor used to wind pickups. The insulation is usually some type of covering such as polyester, polyvinyl formal or a varnish, also called enamel.
The most popular magnet wires used are Plain Enamel (PE), Polyurethane (P), Polyurethane Nylon (PN) and Heavy Formvar (HF). The most commonly wire gauges used by custom shops are typically 41,42, 43, and 44. Personally I also use 42.5 gauge poly in combination with my Alnico 6 to obtain a totally unique tone. A nice compromise between 42 and 43.
Magnet wires come with different type of insulation and sizes.
Plain Enamel (PE) - Plain enamel has a very distinctive brownish-purple color and is insulated with a film of conventional enamel (varnish). This is one of the very first protective coating invented and used to insulate magnet wires. Enamel requires mechanical stripping prior to soldering. It is also very inconsistent in its overall thickness, making it difficult to control variables such as DC Resistance. This wire was used in vintage pickups in the '50s and '60s and is widely used today by custom pickup shops.
Polyurethane (P) and Poly Nylon - These two types of insulation are almost identical. Polyurethane-nylon combines the magnet wire insulation characteristics of polyurethane with the advantage of a nylon topcoat. Both are highly consistent and readily solderable. In addition, the nylon provides improvement and allows for a better scrape resistance in the winding operations.
Heavy Formvar (HF) - Heavy Formvar magnet wire is insulated with vinyl acetal resin and has a smooth uniform film. Its insulation is twice as much as the other type of wires and with a thickness of .0004” the film can withstand excessive elongation without rupture. A lower capacitance will be possible due to the thickness. This will allow higher frequencies to cut through the mix better.
How a coil is wound has a direct effect on how a pickup sounds, as well as how many wraps are used, and what gauge of wire is used. Thinner wire means increased resistance. With the same number of windings, a thinner wire will make a smaller coil. When the number of windings is increased the pickup will be louder. Overwound pickups are a popular request among guitarists who are seeking a higher resistance, therefore a hotter pickup.
Note that more winds will give you a warmer tone with less high end frequencies and, underwound pickups will also give you a tone that is slightly brighter than overwound pickups.
When talking to a pickup builder it is much more important to describe the tone you are looking for than asking for a specific resistance or capacitance and so on. These technical specifications will be addressed once you have determined how you want you pickup to sound.