It has to do with the maximum length loaded round the action will handle (in design mode). For the Remington 700 the short action sill take loaded rounds of the 2.80" range (308 Win, 223 Rem, 243 Win). The long action will take the longer loaded rounds 3.340" range, (30.06, 300 Win mag, 375 H&H).
Well it looks as though nobody has opted to respond. The long and short of it is just that, the length of a bolt action rifles action or receiver assembly. Of course, the bolt coinsides with the length as well. Manufactures such as Winchester i.e. Repeating Arms and Remington for example manufacture calibers in both lengths. Example: Winchester Mod. 70 in .30-06 is a long action and the same model rifle in .308 is a short action. To understand why a company manufactures different lengths of ammo, you'd want to investigate the history of each round. Most shooters concern for whether is a long or short action is mainly when parts for that rifle are being purchased. If you were investing in a different stock for a particular model, you'd either specify the caliber or whether it's a long or short action. Otherwise, the action, barrel, ect... would not fit properly. Another reason would be if you're in the market for optics bases. One piece assemblies would be different between the two. This hopefully answered your question.