I don't know much beyond the fact that they came out in .32 in 1903 and in .380 in 1908 (Someitimes confusing, that is the same year as the .25 ACP.) Colt made hundreds of thousands of them, probably more than Savage, Remington, and S&W combined. There are 4 main variations, 4" with a bushing, 3.75" with a bushing, 3.75" without a bushing, and 3.75", no bushing, with a magazine disconnector. Many minor variations to keep collectors happy. I figure the grip safety is to keep folks comfortable with the concealed hammer. The hammerless Remington had a grip safety, the Savage with exposed striker lever that looks like a hammer does not. A good shooter and a neat design. There was a big 1903 in 9mm Browning Long for Sweden. Most of them you see here have been ruined by bushing the chamber to .380.
Now let me tell you about the 1910 9.8mm Colt and the FN Gran Browning 9.65mm. Browning/Colt/1911 action guns scaled down to those odd calibers. Gorgeous. Wish they had made more than 3 Colts and some very few FN prototypes.