In real life, the Shotgun is a legendary weapon, known for extreme power at close range, noise, recoil, and a large shot spread (whenever convenient for the movie maker), due to the fact that it fires multiple pellets at once. Whether or not these things are true, the shotguns in the game certainly live up to people's expectations. In the game, there is a wide variety of shotguns, from the Judgement, a shotgun with excellent range, insane power, but low RoF and ammo capacity, to the USAS 12, an automatic, medium power, medium capacity shotgun.
Rapid Fire Edit
Jackhammer, USAS 12, KSG, 1216: These shotguns are full or semi auto, and much weaker than pump-guns. All have very fast reloads, and have lower range than pump-guns. With these shotguns it is possible to attack grouped enemies, as they have fast RoF and reloads.
High Power Edit
Judgement, R870, SPAS 12, Neostead: These typically have good range, very high power, and low RoF and ammo capacity. They will kill most opponents in one shot, but if you miss, you will likely die before you can reload. With these shotguns it is rarely wise to take on multiple opponents at once, instead take 'em one at a time and you'll be fine.
Note: While the Neostead is a two round burst gun, it fits with pump-guns better because it fires the two rounds so fast it's more like one shot.