From Wikipedia: http://en.wikipedia.org/wiki/Apocalyptic_and_post-apocalyptic_fiction
Apocalyptic fiction is a sub-genre of science fiction that is concerned with the end of civilization either through nuclear war, plague, or some other general disaster. Post-apocalyptic fiction is set in a world or civilization after such a disaster. The time frame may be immediately after the catastrophe, focusing on the travails or psychology of survivors, or considerably later, often including the theme that the existence of pre-catastrophe civilization has been forgotten (or mythologized). Post-apocalyptic stories often take place in an agrarian, non-technological future world, or a world where only scattered elements of technology remain. There is a considerable degree of blurring between this form of science fiction and that which deals with false utopias or dystopic societies.