The shotgun was developed to shoot game on the wing/ run. Birdshot from size #9, the smallest, to BBB and T size, the largest, are used to shoot birds on the wing or small game while running. Many think that shooting birds on the ground or small game such as rabbits while standing still with a shotgun is not sporting.
Shotguns are also used to shoot deer with buckshot for two reasons. On deer drives with dogs because the deer are running and because the shot does not travel far and will not hit other hunters. Buckshot is also used in very populated areas for the same reason. Buckshot will kill a deer out to about 35 - 50 yards depending on size of buckshot and choke used. Buckshot is offered in #4 buck the smallest to 000 buck the largest. #4, #3, #2, #1, 0, 00, and 000 buck is offered by the big three Remington, Winchester, and Federal.
Buckshot is also used by the police, armed forces and regular folks for home defense. The pump is the most popular followed by the semi auto. The police use short barrels 12-18 inches to fit in tight places. Their guns are choked clyinder bore or inproved cylinder. They use them for close combat under thirty yards with buckshot or out to 50 yards with rifled slugs.The armed forces also use shotguns for close combat but as of late they are used as entry tools to shoot off locks and such.
For home defense many prefer #1 buckshot as a compromise between shot size, number of pellets and penatration. Your results with you gun may vary.
Shotguns with slugs are also used to shoot deer in populated areas. There are two types of slugs, foster stlye better known as "rifled slugs" although they are not realy rifled, are used in smooth bore barrels. The second is "sabot" slugs. These made to shoot in fully rifled barrels or with rifled choke tubes.
Remington, Mossberg, Winchester, Federal, Benelli, Beretta, Browning all have great web sites that explain a lot. Start with the Remington site and go to the reading room. Lot's of downloads and FAQ's. MIKE.