Shotguns are one of four weapons that use the Firearms skill. They tend to do multiple small-numbered dice worth of damage (usually something like 4d5 or 4d6), meaning that they have a higher minimum damage than a pistol, but a slightly lower maximum damage. As with all guns, shotguns are not worth using unless your Firearms skill is high.
Shotguns can use both bullets and energy cells as ammunition.
Shotguns, unlike most ranged weapons, are actually most powerful at close range rather than long range (10-06-03). This makes them useful as a complete alternative to melee combat, since it won't fail you at point blank.
Both shotguns and machine guns look the same in appearance. (Elona+ adds a new sprite for Shotguns.)