Many people get confused about magnum rifles and pistols, and magnum shotguns.
Magnum rifle and pistol rounds have more power and higher velocity.
The modern standard shotgun shell is 2 3/4 inches long. The 3" shell is....3 inches.
Magnum shotgun shells just have more shot. For instance, a standard load of #00 buckshot is 9 pellets. A Magnum load is 12 pellets, and a 3" shell holds 16 pellets.
Magnum shells put more shot into the air. The shot isn't going any faster than standard shells, and doesn't carry any farther.
What you gain is more shot = a better chance of getting hits on target. The minus, is increased recoil and blast = loss of speed and controlability.