There is a lot of confusion because there are two different pistols called the "Model 1903" by collectors. (Colt never used those model year terms; collectors use them for convenience.)
The first is a dual link, recoil operated pocket pistol, a shortened version of the Model 1902. It has an exposed hammer. It is chambered in .38 ACP and was never made in any other caliber. Colt called it the pocket pistol (hammer). That model is the one being discussed and is relatively rare; it was never used or purchased by any military force.
The second is a blowback pocket pistol, with no visible hammer, chambered in .32 ACP. It was never chambered in any other caliber. A very similar, but not identical, model, which collectors call the Model 1908 pocket pistol, was chambered in .380 ACP. Both pistols are fairly common, with almost a half million .32's made. Both pistols were purchased in limited quantities by the armed forces and other government agencies during WWII.