The major amp designs are Class AB and Class D, as most other car amp classes are variations on these two designs.
-- Class AB amps: low distortion and high reliability, usually from a larger chassis. AB amps are not very efficient, losing about half their power to heat.
-- Class D amps: higher efficiency, less heat, and less current draw than AB amps, and their compact size makes them a great choice.
-- Other Classes either combine Class D operation with Class A or B design, or use exotic voltage-boosting circuitry to amplify the sound without taking up too much power from the electrical system.