As Mudbug mentioned, it is simply the 32 S&W Long with a different headstamp.
Around the turn of the century, Colt was transitioning from their, inferior, outside lubed heeled bullet cartridges to modern inside lubed designs. But, the direct logical design/step had already been taken by S&W.
As a direct competitor, Colt didn't like marking their guns with S&W's name. So, they cheated, the 32 S&W Long became the 32 Colt New Police, the 38 S&W became the 38 Colt New Police and the 38 S&W Special became the 38 Special (sometimes seen as 38 Colt Special).
Conversely, at the time, S&W didn't chamber their guns in any Colt cartridge.
As to the alleged difference, at the time, S&W only loaded a round nose bullet and Colt decided to only load a flat point. Other than that, the exact same cartridge, same general specs, same performance.
As far as shootable ammo, 32 S&W Long (and 32 S&W)(it shoots both) are readily available at any of the larger chains or on line. Boxes and ammo marked Colt New Police are kind of rare and are collector's items.
MLG