Short and long refer to the length of the action. Different cartridges have different lengths. The long actions are long enough to handle the likes of the .30-06, 7mm Mag, .300 Win Mag, and the like. The short actions handle the .223 Win, .243 Win., 7mm-08, .308 and the like. The short actions are a bit lighter, and have a shorter bolt throw when chambering a new round.
BDL and ADL refer to the finish of the guns. Same action and barrel. The BDL is nicer wood, typically includes a trapdoor on the box magazine, which allows you to unload the gun without cycling the action. ADLs are more plain, may have synthetic stocks, and have a blind magazine, meaning the only way to unload it is out of the top, typically by cycling the bolt.
That's the short answer, anyway.