The .32 S&W cartridge was introduced in 1878 for the Smith & Wesson model 1½ revolver. It was originally designed as a black powder cartridge. The .32 S&W was offered to the public as a light, defense cartridge, for "card table" distances.
The .32 S&W Long cartridge is derived from the .32 S&W, by increasing the overall brass case length, to hold more powder. Since the .32 S&W headspaces on the rim and shares the rim dimensions and case and bullet diameters of the longer .32 S&W Long, the .32 H&R Magnum cartridges, and the .327 Federal Magnum, .32 S&W cartridges may be fired in arms chambered for these longer cartridges. Longer cartridges are unsafe in short chambers, so neither of these longer and more powerful cartridges should be loaded into arms designed for the .32 S&W.
Read more about .32 S&W: Chambered Weapons