In my opinion, one key difference between DF (dystopian fiction) and PAF (post-apocalyptic fiction) is the primary tone of the work. DF evokes feelings of oppression, while PAF evokes feelings of desperation. Of course, characters can be ‘desperate’ under an oppressive regime, and oppressive regimes can emerge in a post-apocalyptic setting. However, I think that there is a distinction to be drawn between the two genres.
To me, the biggest difference between DF and PAF is in the ownership of the means of production. In DF, the primary method of production is owned by some oppressive entity (most frequently a government or corporate entity). Some central polity controls the consumer market through a manipulation of supply and demand, and overt violence generally takes a back seat to political machinations and propaganda manipulations. In PAF, the means of production are wholly non-existent. There is no central polity to enforce a currency standard, and most people will either barter, steal, or live off the land to survive.
For instance, the world of William Gibson’s Neuromancer (1984) is dystopian. Governments, corporations, and wealthy individuals control the means of production, while outsiders like Case and Molly do their best to survive. Although they are by no means well off, neither are they truly desperate. Whether in Chiba, BAMA, or Freeside, the protagonists never have a shortage of business opportunities. This stands in stark contrast to the world of Stephen King’s The Stand (1978). Even though Randall Flagg establishes an oppressive society in Las Vegas, his control is nowhere near absolute. In a truly dystopian setting, we would expect to see his power and influence extend throughout the entire setting. In this way, The Hunger Games blends the two genres. The world of the Capitol is clearly dystopian, whereas daily life in rural Appalachia more closely resembles that of a post-apocalypse. Except for the titular games, and subsequent intrusion of the Capitol into the daily lives of the residents of that district, the setting is largely post-apocalyptic.
Ultimately, the quality of a work will shine regardless of setting. However, I think that it is an important distinction to make when analyzing genre and tone.
K. Julia Stamm