Colt called it the .32 Colt New Police in revolvers it made chambered for the cartridge.
The .32 S&W Long was introduced in 1896 with the company's first hand ejector revolver.
It was introduced in 1896 for Smith & Wesson's first-model Hand Ejector revolver.
The .32 Long is simply a lengthened version of the earlier .32 S&W.
The hand ejector design has evolved some, but with its swing out cylinder on a crane, has been the basis for every S&W revolver designed since.
The cartridge stayed the same, but was now loaded with smokeless powder to roughly the same chamber pressure.
When he was the New York City Police Commissioner, Theodore Roosevelt standardized the department's use of the Colt New Police revolver. The .32 Long is well known as an unusually accurate cartridge.