I first started shooting as a teenager, in Air Cadets. We were trained on Lee-Enfield rifles (probably WW2 surplus) [re]chambered in .22LR. Those were heavy rifles for a new shooter! If I recall correctly, they weighed in around nine pounds.
One thing I had trouble grasping for many years was the names of firearm calibers. It seemed to me the caliber names were at best inaccurate, at worst completely deceptive. So let me help dispel the mystery...
A firearm's caliber is named for the diameter of its bullets. So a .22 caliber rifle has a barrel .22 inches in diameter. Similarly, a .50 caliber has a half-inch barrel diameter. Unfortunately, that's only really theoretically true. Things get a lot more complicated right out of the gate, and we'll look at that.
I suppose in the days of smooth bore muskets, the barrel diameter told the whole story. The bullets were essentially spheres of lead. Given that the density of lead is a constant, and the volume of a sphere is strictly a function of radius, barrel diameter completely described those older bullets.
These days it's a lot more complicated. We now use cartridges that contain both the actual bullet and the powder charge: so we need to describe not only the bullet, but how much powder is behind it. And since we now use non-spherical bullets, the diameter doesn't tell the whole story.
Now we describe bullets by their caliber (diameter) and their weight. Bullet weight is measured in grains, one grain weighs 1 seven-thousandth of a pound. So if you're shooting 115gr 9mm Luger ammunition, you're shooting bullets that weigh 115 grains, or 0.26 ounces, or 0.016 pounds. In other words, they have a mass of 7.37 grams.
But unless you're just buying bullets (for example, you're reloading), you're not buying just the bullet, but the cartridge it comes in. This gets even more complicated, because the size and shape of the cartridge is at least as important as the caliber of the bullet. Guns are manufactured for a specific cartridge, and in general it's a really bad idea to try and use a different type of cartridge in there.
Cartridges are named by many different conventions, and it's not always easy to interpret what those names mean. When I was small, hunters would talk about their "thirty odd six" rifle, and I had no idea what that meant. What they were really saying was "thirty-ought-six", or ".30-06". This is the cartridge the U. S. Army adopted in 1906, and it's a .30 caliber. So it's the .30 from "ought six", or ".30-06".
Many cartridges are named for their original manufacturer. Savage Arms invented the popular ".300 Savage" round, a .30 caliber cartridge for the rifles they manufactured. Since Winchester invented the ".30-30", sometimes those are called ".30 Win" or even ".30 WCF" (meaning .30 caliber Winchester center-fired).
I remember growing up, hearing about a "thirty, thirty Winchester". That is, a Winchester rifle that takes".30-30" cartridges. The ".30-30" means a .30 caliber bullet with 30 grains (0.069 ounces) of [black] powder. Similarly, a ".45-70" is a .45 caliber bullet with 70 grains of powder. Both those cartridges come from the end of the 19th Century, when the U. S. Government designated cartridges by their caliber and powder charge.
A lot of rifles are chambered in ".308 Win", or the .308 caliber Winchester cartridge. Military rifles might use a "7.62X51mm NATO" cartridge, which is almost exactly the same thing as the .308. If you do the math, you'll find 7.62 mm is .30 inches. Along similar lines, the AK-47 shoots "7.62X39mm", or a .30 caliber cartridge that's 39mm long.
There are other designators that are used. "Magnum" means over-sized, so when someone talks about a ".357 Magnum", they are referring to a cartridge with a .357 caliber bullet that's "oversized", which means it has too much powder. You can also buy ".44 Magnum" or even ".50 Magnum" guns.
Probably the hardest thing for me to understand about ammunition was that the names are really only kinda-sorta accurate. Virtually every ".357 Magnum" will shoot ".38 Special" as well. I never understood that, as .357 inches differs significantly from .38 inches. It turns out the .357 Magnum and the .38 Special have the same diameter: .357 inches. The .38 Special was apparently marketed as .38 caliber, because the cartridge itself was .38 inches in diameter, even thought the bullet was only .357 inches.
Marketing is probably the hugest driver for cartridge names. If you do the math, you'll see that .38 inches is 9mm; but a "9mm" round is quite different from a ".38 caliber" round: they're the same measurement, but the names imply very different specifications. When someone says they have a "9 mm" pistol, they generally mean it shoots "9mm Luger" cartridges. If someone has a ".38", they generally mean a ".38 Special".
In the end, when I was told many years ago that "caliber" means "diameter in inches", that's not really the whole story. Cartridge names are really a sort of branding: they refer a specific, detailed design. Diameter is a huge part of that, but there's a lot more to it than just bullet diameter.