.32 S&W cartridges can be fired safely in a firearm that is chambered for the .32 S&W Long. There is also a .32 colt short and long combo that is not interchangeable with the S&W ammunition. It will definately not hurt your gun, but the shorter ammo will leave residue in the chamber that makes it difficult to insert the longer shell without a good cleaning. This is not a big deal, the same thing happens when you shoot .38's in a .357 mag. Go ahead and shoot those cartridges then clean the cylinder with a wire brush. Those rounds can also be safely fired in guns that are chambered for .32 H&R Mag and the .327 Federal Mag.
http://en.wikipedia.org/wiki/.32_S%26W_Long