Cartridge names are a unique and interesting field, and can be very confusing but there are some general rules, and then there are specific exceptions.
The one rule that everyone follows is the cartridge name has something to do with the people who first made it. Beyond that, lots of different things happen.
Start in the earliest days of cased ammunition. There are no official standards. Eventually a general custom about names developed, in the US, and another in Europe. And those changed, over time, as well.
With rimfire rounds, the very first were for indoor target shooting, and essentially were a lead ball (BB) in a modified percussion cap, making a complete round of primer only powered ammunition. Today we call the modern version the BB Cap. A conical bullet with a tiny bit of powder is a CB Cap. Heavier bullet, longer case, more powder, its the .22 Short. Same bullet, longer case, more powder, its the .22 Long. Heavier bullet, more powder, it became the .22 Long, Rifle (.22LR and the most popular of all, today)
With centerfire rounds, its a bit different. The system evolved, and besides the maker's name, it included the (nominal) caliber, powder charge, and bullet weight in grains. .45-70-500 Govt is an example. .45 Cal, 70gr powder, 500gr bullet. after some use, the last number got dropped, and its just the .45-70 today. Other rounds from that era follow the same general practice, caliber and powder charge (black powder). A few of the later smokeless powder rounds kept this practice as part of their name, but the actual amount of powder could be different from the name. (.30-30 and .30-40 Krag are a couple of examples)
Pistol rounds were about the same, but different...(yeah, I know,
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the difference was in the relationship of the caliber number in the name to the actual bore and bullet size of the guns. And this changed again with the introduction of the inside lubricated bullet. Won't cover all the details here, but this is the reason our modern .38s are actually .36s (.357") and our .44s are actually .43s (.429")
More modern rifle and pistol round names are more closely related to something about the bore, or bullet size, generally. The .30s are the land diameter of the barrel (.300) while the .308s are the groove to groove diameter of the same barrel (.308") for example.
Europeans used the metric system, both bore/bullet size (could be either) and case length in mm to describe the round. This is 9x19 or 8x57mm. Rimmed cases had an R at the end of the name, 7.62x54R (R stands for rimmed, NOT Russian)
and then there are the exceptions to the general practices, which, you pretty much just have to learn as stand alone things. The .30-06 is one. Unlike the old .45-70, .44-40, .38-55, etc black powder rounds the .30-06 is NOT a .30 cal with 06 gr of powder. IT is the .30 cal, adopted by the US GOVT in 1906.
other exceptions are the .250-3000 and the .22-250 Varminter/Remington.
The .250-3000 Savage was the first commercial round to hit 3000fps, so they put that in the name. The .22-250 is a .22 cal round, made from .250Savage cases (originally, and as a wildcat) The .22-250 Rem is the wildcat .22-250, adopted by Remington and standardized.
.22 hornet, .218 Bee, .219 Zipper, .221Rem Fireball, .222 Rem, .222 Rem Mag, .223 Rem, .224 Weatherby, .225 Winchester, .22-250, and .220 Swift ALL SHOOT THE SAME .224cal BULLETS.
The difference in caliber numbers is for marketing. Each one has a different size case, some rimmed, some not, and each one gives different velocities, but all shoot the same bullets.
Confused yet???
it gets even worse when you look at the British system....
In the US, when a new round is made by taking an older one and necking the case up, or down, the new caliber is the first number, the parent case is the second. The British do it exactly the other way around. Maybe that's because they drive on the "wrong" side of the road, I don't know...
So, there are several different systems in use, and they overlap. And there are exceptions to the systems as well. A fun area of study for some, and one that teaches the history of cartridge development along the way.
Reloading manuals usually have a short history of the rounds, a fair place to start. Cartridges of the World is a good reference, but is known to have errors.
If you want chapter and verse in detail, there are several good books, and cartridge collectors who can tell you more detail than you probably want to know.
Hope this helps, but understand if it only confuses you worse!