This is true but, as I related to her in our subsequent conversation, this is not the same thing.
Most dystopians take place after or during an apocalypse this is true, which makes it very hard to suss them out of the post-apocalypse genre.
But what I truly love about the post-apocalypse is not present in most dystopian literature: hope.
There is little of this to be found in, say 1984 or Children of Men, though the movie of both do add a glimmer of hope.
I have often compared the post-apocalypse to Europe's dark ages after the fall of Rome, in which technology literally took 1,000 years or so to regain its former level in many fields (especially architecture).
To continue that analogy, its more accurate to say I love the Renaissance than the Dark Ages.
In the Postman (the book- get that awful Costnerian tripe away from me) a lone rogue/entertainer/con man inadvertently sparks a rebellion through the simple act of delivering mail.
In Star Man's Son, a rejected scout and his mutated cat leave their tribe on a quest of exploration and wind up uniting several tribes together to face a larger threat.
In Showtime's amazing series Jeremiah, a pair of wanderers attempt to drag a powerful, reclusive group of survivors out of their bunkers to begin the task of aiding and rebuilding disparate groups.
In Fallout 3, Three Dog has taken to the airwaves to encourage his fellow man to "fight the good fight".
In the corner of Darwin's World that I got to develop, the Fertile Crescent, I was frequently told to make things more bleak. My original design docs had things on the verge of getting much better too quickly.
In short, what interests me is how things come back together.
About the only dystopian work I truly love is 12 Monkeys. The future is exceptionally bleak, with small groups of humans living underground to hide from a never-ending plague above. But a) there is hope and b) even in the glimpses of the dystopian future we see, Terry Gilliam makes the darkness so absurd its practically a black comedy.
I would also like to amend this post with a recommendation for Star Man's Son. This Andre Norton Post-Apocalypse book is out of print, but copies from the 60's and 80's are still available relatively inexpensively from Amazon.
It's a great post-apoc tale about the Arthurian-esque journey of a lone wanderer and his mutant, empathic mountain lion. Great stuff.