Choosing Pickups
Contents
Single Coils vs. Humbuckers
One of the largest issues involved in magnetic guitar pickups is that they are prone to picking up interference, such as from flourescent lights or radio signals. This produces hum and noise. Single coil pickups use one coil, whereas humbuckers use two coils wound in opposite directions. Humbuckers pick up the interference, but with opposite voltages in each coil, causing the interference to cancel out. This is why they are called humbuckers - they have less noise and hum than single coils. This is the main difference between the two.
Humbuckers also have more output than single-coils, which can make them more easily push an amp into overdrive/distortion. In the modern world, this isn't much of a feature - most amps now feature powerful pre-amp drive. Or you can resort to a fairly cheeap boost pedal to make the signal hotter. Humbuckers main benefit is their higher signal-to-noise ratio. Distortion tends to add noise, so it's helpful to start with a rather clean signal, or things can quickly become a noisy mess.
Yet, single-coil and humbucker pickups have different tone. This is mostly due to their impedance. Pickups have a resonant peak, a frequency where they are most responsive and have more output. Beyond the resonant peak, pickups get worse and worse at reproducing those frequencies. Single-coils have a higher resonant peak, and thus have a certain "shimmer" to their tone. They are described as glass-like. Humbuckers, in contrast, sound a bit nasal.
Parallel-wired Humbuckers
The above descriptions refer to humbuckers wired in serial, which is the most common way to find them. The ending terminal of one coil is wired directly to the beginning terminal of the other coil. However, many manufacturers provide "4-wire" pickups. Each coil is wired independently, and the customer is given the two endpoints for each coil (hence 4-wire). You are free to wire each coil as you like.
One way to wire them is in parallel. This makes them sound similar to single coils - they have the lower output and higher resonant peak. But at the same time, they still cancel hum/noise from interference. Because they are capturing the string at two "points" as opposed to the smaller one "point" of a traditional single coil, there may be some high frequency cancelation (due to a comb filter effect), so they won't sound exactly like a single coil. But it is rather close.
The point here is just because it's a humbucker doesn't mean it has to sound nasal.
Many guitars that feature single-coil pickups have them wired so that the pickup selector can select two-at-once, with the selected pickups have opposite direction coil windings. This effectively makes them operate as one big parallel humbucker - single-coil tone with hum-canceling. This is how the Fender Stratocaster is wired for pickup selector positions 2 and 4, which happen to be very popular positions.
Stacked Humbuckers
Also, appearances can be decieving. Most humbuckers have two clearly visible coils or are cased but clearly wider than a single-coil. However, some pickups look nearly identical to single coils but are actually humbuckers. The two coils are stacked on top of each other, creating the appearance of a single coil. Many times the goal is to get hum-canceling, not the more nasal and higher output humbucker tone; so they are wired in parallel. Yet, this is not always the case, and you have to be careful when selecting your pickups and/or wiring them, depending on what you want.
Position
The position of the pickup also has a big impact on tone. A guitar typically has 2-3 pickups, labeled bridge, middle, and neck relative to their position being closer to the bridge or neck. Bridge position is very bright and tight - it is very responsive but can be a bit harsh in the high frequencies and can be a bit thin or nasal. Neck position is more loose and open, with a thicker bass response and a more hollow tone. Middle is...in the middle.
Manufacturers often create pickups as a set, with different models for the neck and bridge to provide a more consistent tone when switching between them. This doesn't mean they have the same tone - it's impossible to get the same tone given that they are "looking" at different parts of the string, which physically must behave differently. And it makes the guitar more versatile to be able to use the different positions. The goal is to try to make the output levels consistent, as well as not have one sound dramatically different from the other.
So part of the purchasing process is determining if you want to replace all your pickups with a set or specific ones and doing research to see how well the new pickup will match the remaining ones for other positions.
Also, if you just want one pickup, make sure you are getting the neck/bridge version you want - they may have the same name. For instance, John Petrucci uses a Dimarzio Crunch Lab in the bridge position and Liquifire in the neck position. These pickups have no neck/bridge variants, so you know exactly what you're getting. But if you wanted to get a Dimarzio Gravity Storm pickup, there's a Gravity Storm bridge and a Gravity Storm neck, which are very different pickups.