What Treo said. BUT...
It's worth mentioning that "9mm" typically refers to 9x19mm. Which is also referred to as "9mm Para," "9mm Parabellum," and "9mm Luger." These are all the same cartridge - this is a VERY common caliber.
9x18mm is also referred to as "9mm Makarov" - this is used in mostly Soviet, Hungarian, and Bulgarian pistols, many of which were imported in the 1990s.
9x17mm is the same cartridge as .380ACP. Very common cartridge. It's almost always sold in the US as .380 though, almost never as "9x17mm"
9x20mm is the "Browning Long" cartridge and is obsolete. If you have a vintage Browning pistol that uses this caliber, you're outta luck for cartridges, and will need to learn to custom cut your brass cases and do your own reloading, if you want to shoot the thing.