Yes, they are generally called "Shorts" by most people as they are shorter than the 32 S&W Long. Their actual name is simply 32 S&W as they were developed first. After the Long cartridge was developed it was probably inevitable that people would refer to the 32 S&W rounds as "Short" since there was a "Long", never mind what the actual manufacturers name was. After years of being in the gun & ammo business you get used to improper names for ammo (and trying to be sure the customer gets what they actually need whether they know the proper name or not).