The fine line? That's tough. All genres can be debated over.
However, there's some general lines. First, I think you meant to say post-apocalyptic.
Dystopian is typically a society that's the opposite of a utopia: think the Giver and Hunger Games. While Hunger Games was set after a devastating war, the plot has to do with its dystopian nature.
Post-apocalyptic looks at the world after its fall. Think Walking Dead. They may visit dystopian societies throughout the story, but the plot has to do with its post apocalyptic nature.