As our referenced quote states in SFMZ's Sci-Fi Subgenres A to Z feature, Apocalyptic features holocaust-like stories focus on the end of the world, or the world just after the end. This sub-genre usually tells the story of humanity's struggle to survive after some form of devastation. The world may be wiped out by plagues, wars, or astronomical bodies, but however it happens, these stories focus on how we cope and the ways in which we rebuild society.
Post-apocalyptic stories are set well after some vast upheaval. Rather than showing the immediate aftermath, these tales depict a new society that has arisen from the ashes, usually here on Earth. Often the survivors remain leery of technology. Post-apocalyptic often take place in an agrarian, non-technological future world, or a world where only scattered elements of technology remain. This sub-genre grew immensely popular in the late '70's and '80's portraying a band of survivors endure tremendous hardships.