Wiki DOES have a good intro. However, remember that cartridges get named by people that want to sell them, so names can get screwy. The.38 Special and the .357 Magnum BOTH use a bullet that is .357 inches in diameter. There is the 9mm Makarov and the 9mm Parabellum that do NOT share a common bullet size. Shotguns have shells measured in GAUGE, not caliber (except for the .410 shotgun, which IS a caliber) Gauge is based on the number of round lead balls that just fit the barrel that total up to one pound. So a 10 g would have a ball weighing 1/10th of a pound, a 12 g 1/12th, a 20 g 1/20th, and so on.
A name may be added to the numbers to designate a different cartridge of a similar size, different shape, such as the .300 Whisper, the .505 Jeffries, etc.