9mm Parbellum is the correct name- sometimes called 9mm Luger. 9mm NATO IS a 9mm Parabellum with a specific bullet/powder. All these are also called 9x19, in light of the 19mm long case.
Do NOT use any other 9mm catridge- there are about a dozen. Most are obsolete, rather obscure, collector's rounds, but 2 are common- 9mm Corto (or Kurz) which is the .380 ACP, and the 9mm Makarov- which is another round altogether.