Here's a quick rundown on common 9mm cartridges and their aliases. Some of these aliases you might never see used other than a site like TFL.
These are the same cartridge: 9x19, 9mm Luger, 9mm Parabellum.
These cartridges are the same: .380 ACP, 9x17, 9mm Browning Short, 9mm Kurz, 9mm Corto.
These cartridges are the same: 9mm Makarov, 9x18, 9mm Soviet
These cartridges are the same (BUT DIFFERENT FROM THE 9mm Makarov!): 9x18, 9mm Ultra, 9mm Police. This round isn't commonly encountered, and virtually all uses of 9x18 in the US refer to the 9mm Makarov round.
There are quite a few other 9mm rounds out there that are less frequently (if at all) encountered, such as 9mm Stery, 9mm Mars, 9mm Winchester Magnum, 9mm Glisenti (same case as the Luger, just less powerful), 9mm Largo (or Long), etc.