For historical reasons, many caliber designations are followed by a suffix that positively identifies with specificity the size of that ammunition. Remember that the beginning of the caliber name (9mm, .45) only indicates the diameter of the bullet, not the length of the cartridge. After all, the AR-15 fires the same size bullet as a .22 pistol, but many times faster.
ACP = Automatic Colt Pistol
MAG = Magnum (high power)
S&W = Smith & Wesson (developer of that caliber)
SIG = SIG Sauer (developer of that caliber)
SPL = Special
LC = Long Colt
LR = Long Rifle (.22 LR is also used in pistols; it is a standard)
While there are limited exceptions with revolvers, semi-automatic handguns never fire more than one specific caliber, so it is important to get this right.
Example: .357 Mag is not the same as .357 SIG.
In many cases, you have no options: the most common revolver caliber is .38 SPL. You can no longer easily find any .38 ammo that is not Special, so you have only that choice. However, in 1898, most revolvers fired a weak cartridge called .38 Short. With further development, that was followed by .38 Long, and finally .38 Special. That has been the standard for about 80 years, and is unlikely to ever change. There are people who collect, and shoot, historical weapons, so there are companies that make obsolete ammo for those people. A Google search for “.38 Short ammo” returned 396,000 results. While it is unlikely you would find any .38 Short in a gun store, it is possible, so looking for the designation “.38 Special” simply gives you confidence that you have the correct ammo.
If you have a .45 semi-automatic, that ammo will be described as .45 ACP. Don’t confuse it with .45 LC (AKA .45 Colt). That is used in cowboy-style single action revolvers.
If you have a .380 pistol, this is simpler. Or is it? I’m not aware of any type of cartridge for the .380 that is not marked “.380 ACP”, except that European ammo for this 9×17 cartridge will often use terms like “9mm Browning” or “9mm Kurz”. I once used a dealer to transfer an old pistol marked “9mm Browning”, and the clerk didn’t know that it was actually a Czech .380.
Speaking of the famous 9mm, there are at least 9 cartridges extant that can be called 9mm. The standard throughout the world is 9mm Luger (also described as 9×19), but there are minor variations like 9mm Makarov (9×18), 9mm Ultra, 9mm Police, 9mm Browning (9×17), 9mm Steyr, 9m Largo, and others. Some of these are aliases for what we know as the .380, and some are obsolete. If you have a 9mm handgun that is less than 30 years old, it will be a 9mm Luger, and it should be marked “9×19”.
Clear as mud? Sorry. Obsolete firearms and ammo never go away, they just fall out of favor. If you are new to shooting, you should not be fooling with 80 year old firearms until you are certain what ammo it uses. However, if your gun is less than 30 years old, there should be no problem at all. Terms like .22, .380, .38, 9mm, .40, and .45 are very standardized now. If in doubt, research, or ask.