Today, firearms use very specific calibers and cannot operate with cartridges they are not designed for. When looking at older firearms - muskets, aquebuses - it is hard to determine whether they had any standardized caliber and I have never found mention anywhere of, say, the caliber of firearms used by a faction of the Thirty Years War. When was caliber standardized between weapons? And in the period before that, was ammunition for firearms idiosyncratic, with each gun having its own ammunition that would only by pure chance fit another weapon? Or was there no real concern for bore, and balls would just be used for any weapon they would fit into? Further, it would seem on sight that pre-modern pistols and longguns have the same (range of) caliber. When were pistol and rifle calibers differentiated? And was there a concept of an "in-between" caliber/weapon akin to the modern concept of the intermediate cartridge?
OK: first, it's hard to say there's ever been an agreement on what to actually CALL the caliber of something. 357 Magnum and 38 Long Colt have the same diameter bullet. 401 Powermag has a bullet that's really .401, but 400 Whelan is .405. Browse Barnes' Cartridges of the World ( a good reference) and you'll see the caliber of something can be bullet diameter, bore diameter, land-to-land diameter of the rifling, or...whatever. I am also not sure if you can totally differentiate between pistol cartridges and rifle cartridges- 44 Magnum is awfully close to a high-powered rifle cartridge, and people are making pistols that use .410 shotgun shells. Generally, smokeless-powder age pistols are loaded differently than rifles, as they have shorter bores and so need faster burning powder, and the bullets are shorter and lighter, the velocities less because the guns aren't as strong and need lower pressure, because they're typically shorter range...but it's not a hard and fast concept: 44-40, and 44 Magnum have been both popular rifle and pistol cartridges.
The old system was for bore or gauge: a 12 gauge gun ( and your 12 gauge shotgun today) would fire a ball that was a 12th of pound, but there would be small variations in actual bore size. For an army, you can imagine there would have to be some standardization- no point to casting bullets of many different sizes, trying to keep track of who's using what. Army-wide national standardization seems to have arrived, though, pretty late. I am not totally clear on what countries adopted what standards when, but in the English North Atlantic colonies, militias had guns made for them to their own specifications, and there were many variations. I think it was also common for English commanders to outfit their units with whatever gun they wanted- but I do not know how common this was, government rules and guidelines, etc.. By the 18th c. there were the "pattern" muskets like the Brown Bess that had the same bore size, but the Bess was not the only gun used by the British Army, and so there were some tragic mistakes. In the Battle of Waterloo, a desperate attempt to re-supply the defenders of LaHaie Sante was futile because they'd brought the wrong ammunition. Even in the American Civil War, there were newer .58 caliber rifles used by the Union along with older .62 caliber muskets, and .54 caliber breechloaders.
There can be a little wiggle-room for the size of the ball in muzzle-loaders. In an earlier round-ball musket, it was a somewhat loose fit- as powder fouling built up, the ball would tend to become a tighter fit, so that was fine. Later ones using conical bullets had to be more precise, but for round-ball rifles, different thickness patches can make up for slight differences in bore and bullet size. Anyone who bought a sporting gun from a gunsmith would get bullet mold to match, to cast bullets. A gunsmith would ream his barrels to use that size bullet, but any gunsmith could also make a new bullet mold cherry, to make a bullet mold for another caliber gun.