Postapocalyptic tabletop RPGs are a small but notable niche subgenre, with their influence perhaps most felt via Fallout – which, whilst a CRPG, was very much developed with a tabletop game fan’s sensibilities (right down to the designers originally planning to use GURPS as the underlying system before their agreement with Steve Jackson Games fell through). The forefather of them all is, of course, Gamma World – but Gamma World tends much more towards the sillier end of the postapocalyptic setting spectrum, with very unrealistic, borderline cartoonish mutations being very much the order of the day.
As such, the first clutch of games to come out following Gamma World all seem to have positioned themselves to try and offer a more serious-minded approach to the subject matter – and interestingly, they all have different ideas as to how long after the initial civilisational collapse the game should be set in. 1980’s The Morrow Project followed Gamma World in setting itself a comparably long time after the big kill; the specific conceit of the game is that PCs are all volunteers in the titular continuity-of-civilisation project, cryogenically frozen when it looked like things were about to go to shit with the intention of being thawed out after a reasonable time period had passed so that they could take the lead on rebuilding, only for the cryogenics computers to malfunction and leave them frozen for 150 years.
The major difference between this setup and Gamma World is that whilst Gamma World PCs are way too young to have any personal memories of the time before (and chances are their communities have little to no institutional memory of it), The Morrow Project presents you with PCs who only know the world before, who are able to explore and make discoveries about the postapocalyptic world whilst making full use of the technological knowhow they’ve retained, are perfectly placed to exploit any remaining technological caches they can uncover, and are tasked with restoring order and imposing their values on a hostile present day. (In some respects it can come across as a sort of time-hopping colonialism…)
Twilight: 2000, by comparison, took the opposite tack by presenting a setting in which civilisation collapsed under the weight of Too Much War within the past few years. All the player characters are not only assumed to have lived through the downfall (and therefore have vivid memories of the way things used to be), but are also among the last representatives of the pre-downfall US Army. The events of the Twilight War have been intensely disruptive – but not enough time has passed to cause people to forget that things used to be better, or the values that held sway before the war, and so when the PCs swing by to help a community rebuild it feels a bit less like colonialism and a bit more like humanitarian intervention. (Unless your PCs go bandit, of course…)
In between Twilight: 2000 and The Morrow Project, both in terms of assumed IC time period and in terms of publication date, is 1981’s Aftermath! by Paul Hume and Bob Charrette. This was a game originally prepared for publication by Phoenix Games, who’d also republished Hume and Charrette’s Bushido after its original publisher folded; however, Phoenix went bust in early 1981. Luckily, Fantasy Games Unlimited’s Scott Bizar stepped in to rescue Hume and Charrette’s two RPGs, making them part of the FGU catalogue and, I suspect, substantially increasing the extent of their distribution in the meantime. (The FGU edition of Bushido is easily the most widely-available version on the second hand market, after all.)