Post apocalyptic writing as a genre deals with human society after a catastrophic event, such as war or plague, which has drastically changed the scope of humanity. It is typically set in a world that is devoid of technology or has only a smattering of technology which either not desireable or not accessible to those living. As with many genres, the dystopian and even the science fiction genres overlap with post-apocalyptic writing, so you may have to draw some information from those genres as well.
For example, Ayn Rand's Anthem fits both the dystopian genre and the post-apocalyptic genre and is well-represented on e-notes. Stephen King's The Stand is another example. It is set after a devastating plague but also contains elements of the supernatural as the character finds a way to travel through time zones and across large distances in a matter of seconds. By the Waters of Babylon by Stephen Vincent Benet is another tale that is designated primarily as science fiction but unravels a tale of a young man exploring a city destroyed by a cataclysmic war.
The bottom line is that post-apocalyptic literature is a sub-genre with many characteristics that overlap into other genres. I suppose one way of making a distinction is to focus on the ways the characters survive to rebuild society and a sense of self. The dystopian novels will focus on how these attempts fail in various ways while the science fiction literature will employ obvious elements of "other-worldliness"; you will have to draw these distinctions for your students.