Hi! Here is my explanation of Post-Apocalyptic, Apocalyptic and Dystopian stories/genres as I understand it.
I’ve always looked at Post-Apocalyptic as being after the incident that caused the full collapse of civilization, whereas Apocalyptic are either during the incident or while some of the incident is still going on.
Dystopian to me has active civilization, though in a very negative form that leaves many people suffering. Dystopian is the opposite of Utopian. Utopian is about a perfect world/society. Dystopian is a distorted, unfair, and unjust world/society where many suffer for the gratification of the few (for instance the wealthy)