Split-Coil

‘Split-coil’ pickups are basically double-coil pickups that have been split in two, making one side nearer to the bridge, which gives a slightly brighter tone. This pickup is very commonly used in rock music, and gives an even response over the whole bass.

Single-Coil

As found on the original Jazz Bass, as the name suggests, single-coil pickups have a single coil wrapped around a magnet, and are the simplest form of pickup. They tend to produce a clear bright sound with a strong fundamental (root tone). They sometimes pick up external noise or interference, but if two single-coil pickups are used (as on a Fender Jazz for example), with both volumes set equally, the noise will usually be cancelled out, eliminating the problem.

Humbuckers

Humbucking pickups are essentially two split-coil pickups combined into one unit, with one coil wired out of phase so that any hum or interference is rejected. High frequencies tend to be a little attenuated, but the output is generally ‘hotter’ than a single-coil. The Musicman Stingray was one of the first bass guitars to have a double-coil humbucker situated near the bridge, and was famous for its sound - similar to a Fender Jazz with the bridge pickup turned up full, but with more low end thanks to its twin coils.

Piezo Pickups

Rather than producing a magnetic field, a piezo pickup senses the vibration of the string at a contact point in the bridge of the bass. They are generally used in conjunction with regular electro-magnetic pickups as they tend to sound a lot brighter, and are most often found in semi-acoustic or fretless basses as they do not pick up unwanted noise, hum, or feedback. Without the right kind of amplification though, they can sound brittle and thin.