The I-Frame was the predecessor to the J-Frame and is mainly found in .32 S&W Long and .38 S&W calibers. I-Frames were not made in .38 Special because their frame window is too short to accommodate a .38 Special cylinder. In 1950, S&W introduced the then-new J-Frame Chief's Special (later designated the Model 36) which was basically an I-Frame elongated just enough to accommodate a .38 Special cylinder. In 1997, the J-Frame was further elongated to accommodate a .357 Magnum length cylinder and from that point on, even smaller calibers were made on the new "Magnum" J-Frame.
Even after the introduction of the J-Frame, the I-Frame continued to be produced until 1961 at which point the remaining I-Frame models (by that point designated Models 30, 31, 32, 33, 34, and 35) were redesignated with a -1 and produced on the J-Frame.
The .38 Regulation police was introduced on the I-Frame in 1917 and, as has been mentioned, was chambered for the obsolescent .38 S&W cartridge which is older, shorter, slightly larger in diameter, and much lower in power and pressure than the more well-known .38 Special. The .38 Regulation Police had a square-butt grip and is usually found with either a 3" or 4" barrel unlike its cousin the Terrier which has a round butt and 2" barrel. In 1957, the .38 Regulation Police was redesignated as the Model 33 and, beginning with the M33-1 in 1961, built on the J-Frame. The M33/.38 Regulation Police and the M32/Terrier were both discontinued in 1974.
The .38 S&W cartridge, though once quite popular, has been obsolescent for decades as it was gradually superseded in popularity by the .38 Special. It consists of a .775" straight-walled, rimmed case loaded with a .360-.362" bullet as opposed to the .357-.359" bullet of most other .38 caliber revolvers. It is also quite low pressure with a SAAMI maximum of 14,500 psi as opposed to the 17,000 psi maximum of a standard pressure .38 Special. While no new guns have been chambered for this cartridge for decades, factory ammunition is still available from several makers including Remington, Winchester, Magtech, and Fiocchi. A typical factory load for this cartridge will consist of a 145-146 gr LRN bullet at roughly 680 fps. A variant of the cartridge was used by British Commonwealth military and police forces in Webley, Enfield, and S&W revolvers. This variant is known by several names including .380 Revolver Mk. I/Mk. II/ Mk. IIz or .38-200. It consisted of either a 200gr LRN or 178gr FMJ bullet at roughly 600fps.
If you handload, several people have reported good results by using standard .358" HBWC bullets seated to the same OAL as a factory LRN. While the bullet is undersize, the hollow base supposedly obturates enough to grip the rifling well and give satisfactory accuracy. I cannot personally attest to this practice, however, as my handloading of the cartridge has been primarily focused on 200gr LRN bullets to replicate British military loads in my Webley Mk. IV.