All Sizes and Shapes - - -
Like so many topics, this one is pretty subjective, and has a lot to do with definitions--
There was a time when officers of almost all military services were expected to furnish their own sidearms. After things progressed well into the cartridge era, most were required to choose one chambered for the "standard issue" cartridge. Really, it went farther back than that, for practicality's sake. Why would one choose a percussion revolver that wouldn't accept the military service's paper cartridges that they supplied? And, writing that, I recall several old photographs of personnel on both sides of the War for the Liberation of the Southern Confederacy posing with Colt .31 pocket revolvers, wearing small military style holsters.
There is at one famous image of a Southern officer on horseback, brandishing an early S&W rimfire revolver (No. 1-1/2? No. 2? Whatever the .32 RF with spur trigger was - - - )
For several decades, British officers could carry anything chambered for .455--Thus, the Webley-Fosberry Automatic Revolver was an approved "service sidearm."
And, you could well say that any holster sidearm worn in uniform and supplied by the individual law enforcement officer is/was a service gun.
I personally know two officers who were issued S&W Model 58, .41 magnums when they worked at Amarillo PD some years ago.
The old 1917 S&W was simply a militarized version of the Second Model Hand Ejector. They are lumped in with the N-Frames usually, but were actually a somewhat lighter and trimmer framed revolver. The Colt 1917 was the New Service, which was still being issued by several agencies in the 1940s, and, I believe, into the 50s.
If you limit the frame size to "Medium," as in the S&W Military and Police and the Colt Official Police, you're right--pretty much .38 and .357 only. By the time agencies began issuing sidearms, the .41 Colt DA was pretty much obsolete.
Certain "Indian Agency" police were issued Remington SA revolvers, nickle-plated, with long barrels. Don't know caliber, but they were certainly .44 or .45.
Speaking of personal preference sidearms, at least one old Texas Ranger daily carried a Colt SA in .45 right up to his retirement in the late 1960s. Rangers have always had a lot of latitude in their choice. They are issued the standard DPS sidearm, but can carry 'most anything that meets minimums. Our local Ranger has a SiG somewhere, but he carries a Colt Government Model .45 that his daddy gave him.
When Theodore Roosevelt was Police Commissioner of New York City, he standardized a .32 double action as the police service revolver. I believe it was the Colt, but not sure on this one.
I have no documentation, but have HEARD that the Charter Arms .44 Special Bulldog was issued by some agency, but don't know which. And I read, just today, that the original female Special Agents of the FBI were issued S&W Chiefs Specials, because of their smaller hands. Whoops--these were definitely for concealment, and really don't meet the topic as defined.
Seems I heard of some agency in Alaska that issued .44 Magnums--Not for bad guys, but so the officers might contend with unruly bears. Anyone have any true information on this?
Interesting topic, Nightcrawler.
Best,
Johnny