A zombie is an undead corpse, typically devoid of a soul and with no free will, originating from Voodoo beliefs. In the Fallout world, the term generally refers to ghouls, who very much resemble corpses, often as a derogatory term.
In Fallout 3, most ghouls are very offended by the term. It is commonly used by the bigots who live at Tenpenny Tower, and calling Roy Phillips or Mister Crowley a zombie may lead them to attack the Lone Wanderer. Mister Crowley will hire the Lone Wanderer to kill supposed ghoul bigots by shooting them in the head like they do in old zombie movies.