9x17 is .380 Auto
9x18 is 9mm Makarov, used in the Russian (East German, Bulgarian, Chinese, etc.) Makarov pistols, the CZ82, and the PA63
9x19 is 9mm Parabellum, Luger, etc. and is what most folks mean when they say "9mm."
Pistols chambered in the first two are usually straight blowback designs.
The last generates sufficient pressure that a locked breech design is required.