Firearm ammunition sizing is full of anachronisms owing to historical development and changes in technology. A good example is the .38 Special/.357 Magnum issue. The original .38 “caliber” rounds were “externally heeled”–that is, the base of the round was flush with the outside of the case, hence the bullet was nominally .38 inches in diameter. This was a carry-over from muzzle-loaded weapons where there was no case and the chamber was the same diameter as the barrel. (In currently used rounds, this can be seen in the .22LR and .22WRM cartridges.) In later firearms, the chamber came to be bored out, allowing the bullet and bore to be a smaller diameter than the case, and the bullet came to be fully seated inside the case. Because the case was the same diameter, the .38 S&W and the .38 Super Police (not to be confused with the .38 Super), and later the modern .38 Special continued to be known and nomenclatured as “thirty-eights” even though the bullet diameter is actually .357-.358 inches. When Smith & Wesson developed the .357 Magnum, they used the “correct” size because…well, probably because it sounded cooler, and more to the point from a marketing point of view, was distinct from the .38 Special. The case is IIRC 0.125 inches longer than the .38 Special, not because the extra space is needed but to prevent the round from being loaded into the weaker guns chambered for the .38 Special, permitting one to fire the .38 Spl in a .357 Magnum revolver (though resulting in chamber fouling if this is done frequently) but not vice versa. Note that this is not generally the case even with bullets of the same round; a 9mm Kurtz/.380 ACP round should not be fired in a 9mm Parabellum (9x19mm) pistol, nor should any of the more exotic 9mm rounds (9x19mm, 9x21mm, 9x22mm, 9x23mm, .356TS&W, .38 Super, 9mm Glisenti, 9mm Bergmann Bayard) be fired interchangable with each other, even if you can force the pistol to chamber the round.
The various .30 “caliber” rifle rounds that are common in the US are mostly around .307-.309 inches in diameter. For the most part, Canadian and European-designed rounds whose “calibers” are measured in millimeters (6.5mm, 7mm, 9mm, et ceter) are generally very close to their nomimal values, but the American-designed 10mm Auto is actually .400 inches in diameter, which makes it 10.2mm. (The subsequently derived .40 S&W, originally and dispairagingly referred to as the “10mm Short” during development) is actually correct, as is the .400 Cor-Bon. The .357 Sig round (a .40 S&W case necked down to accept a 9mm bullet) is, like the 9mmP, actually .355-.356 in diameter but is so named to for marketing appeal to law enforcement as a high capacity autoloading replacement for the venerated .357 Magnum cartridge.
By the way, the term caliber does not always refer to bore size; in naval and artillery guns, it referes to the ratio between the length and bore. Gauge, in terms of shotguns, is a measure of the number of balls of equivilent diameters to the bore that would measure up to one pound of lead, which is why shotgun bores get larger with decreasing bore.
So, the reason that the sizings of small arm calibers isn’t specifically because they are arbitrary, but because they were developed by different parties with different standards and/or marketing strategies. There’s really no physical reason, strictly speaking, that a suitable selection of rounds couldn’t be made in standard increments–say, in .05 inch or .5mm increments–with bullet weight, profile and ogive, case configuration, and powder capacity tuned to suit each application, and indeed, this is the case for the proliferation of most modern “wildcat” (custom) rifle rounds which use standard bullet sizes and custom cases–but historically each round was developed at different times, by different people, for different purposes, with no need to commonize on tooling, hardware, or sizes. Today, certain calibers, and within them, certain specific rounds have been winnowed through experience to become the most widely used, with a minority of shooters selecting niche rounds for very specific purposes (or because it’s just cool to shoot some round no one at the range has every heard of) leading to minor but dramatic “religious” arguments regarding caliber selection.
Then there’s the debate among Computer Science graduate students as to what the best round for surviving grad school is; you know what they say: “The tragedy of Galois is that he could have contributed so much more to mathematics if he’d only spent more time on his marksmanship.”
Stranger