Colt made two models for 1903.
The 1903 Hammerless in .32ACP and the 1903 Hammer in .38ACP. The Hammer variant has a 4.5" barrel and looks like a short version of the earlier 1902 Sporting and Military models (both of which were chambered for .38ACP) while the .32ACP Hammerless variant looks almost identical to the later model 1908 (chambered in .380ACP).
Both the 1903 (.32ACP) and 1908 (.380ACP) Hammerless models have approximately 3.75" barrels and fall into the 12.6 prohibited class in Canada while the 1903 Hammer (.38ACP) is just a standard restricted due to the longer barrel and larger caliber.
The FN/Browning 1903 (and Swedish Husqvarna 1907) is a slightly larger version of the Colt 1903 (and 1908) Hammerless models and has a longer barrel and is chambered typically for the 9mm Browning Long (9x20mm) and is in the standard resticted class.
Just a note, too, .38ACP has the same measurements exactly as a .38Super but at a lower pressure. Using .38Super in the early Colt guns will likely result in the destruction of the gun. And just to point out, .380ACP is not the same as .38ACP: the .380ACP is somewhat shorter. The 9mm Browning Long cartridge (9x20mm) can occasionally be found here in Canada as surplus ammunition, but it can also be made by cutting .38Super brass down 0.100" and loading suitable low-pressure rounds (load data is the the difficult thing to find).
As a little bit of trivia, all of these guns were designed by John Browning.
