The term "caliber" is often confused in our language and understanding, even amongst those of us who know better. All cailber means is the diameter of the bore, a 30 caliber bore uses a bullet that is .308 in diameter. What that means is the barrels hole is "bored" to .300", therefore is .3, or .30 or .300 caliber. Then the bore is rifled .004" deep and the resulting groove diameter becomes .308". Others are simular and using either barrel diameter, .300 or .308, is technically correct.
What many of us call a "caliber" is actually not. We often say the cartidge the rifle is chambered for is the caliber but the cartridge is not the caliber. A .30 caliber barrel may be chambered for the .30-30, .308, .300 Savage or Winchester or Weatherby magnum, or .30-06 cartridges. Same bore/groove diameter as anything European OR our military in 7.62 mm. All this means the cartridge is NOT the "caliber" but we often speak as if it were.
Most cartridges have the caliber included in the name but many don't, not corectly anyway. The .218 Bee, .219 Zipper, .220 Swift, .221 Rem., .222 Rem. .223 Rem, .224 Weatherby, .225 Winchester and .22-250 Rem. all have the same barrel groove diameter at .224". But .22 Hornet bores are (or used to be) .223", not .224". ???
Sometimes the caliber implied in the cartride name is marketing hype indicating the bore is larger than it really is, but sometimes it's smaller. A .38 Special and .380 ACP shares the same barrel as a .357 Mag, all three use .357" calibers. (The 9mm is vertually identical, but not quite, at .356".) The .44 Special and .44 Mag share a smaller .429" barrel. But the old .38-40 cartridge (meaning with 40 gr. of black powder) has a .400" barrel, not .357". The Remington .280 cartidge has a bore diameter of .276" and a groove diameter of ..284, aka, 7mm.
European have some add ons for their cartridges which include the case length. The 7.62x39mm, means the caliber is 7.62mm, or .308", and the case is 39mm long. Sometimes they include an "F" or "R" to indicate it has a rim, or "flange" as they call it, but it only relates to the cartridge, not the caliber.
Some American add-ons tell us a little about the cartridge but not the caliber. A .380ACP and .45ACP simply means they are cartridges originally chambered in the Automatic Colt Pistols. Other cartridges were named by the company that first marketed the cartidge. The .243 Win and .270 Win were first marketed by the Winchester company, the .22-250 Rem. and .280 Rem by Remington. Some, such as the .257 Rem. Roberts were named for both the company that made it a factory round AND for the original designer, Ned Roberts. The .30-06, aka, the "Springfield", is a .30 (.308 caliber) developed at the Springfield Amory and adopted by the US military in '06 (1906). The .25-06 Rem means the cartridge is a .25 (.257) caliber that was formed from the .30-06 Springfield cartridge, it was first marketed commercially by Remington after many years of service as a popular "wildcat" , meaning it was a custom chamber job only.
Some, such as the .30-40 and .45-70 were black powder cartidges, with the first being a .30 caliber with 40 grains of black powder and the second a .45 caliber with 70 gr. of black powder. So, it should follow that the .30-30 would be .30 caliiber with 30 grains of black powder, right? Wrong. That was the impression it was intended to give but it's not so, it was actually the first commercial smokeless powder cartridge and it produced same the effect as if it had 30 grains of black powder.
This is not a complete run down on "calibers", or cartridges, in fact, it's just the tip of the iceberg. But, does it all make sense so far?
Well, really, not to me either, it sure don't! It's just something we learn, it takes maybe 10 years if we read a lot. For now, just think of bore or groove diameter as caliber and you will have the crux of it, never mind the cartridge it's chambered for.