Here's the deal with Devil Summoner. There is a Shin Megami Tensei spoiler here, but I won't mask is since knowing it is relevant.
About halfway through Shin Megami Tensei on the Super Famicom, you try to stop US President Thorman from launching ICBMs and obliterating Tokyo. You're unsuccessful and the second half of SMT takes place in post-apocalyptic Tokyo. SMTII takes place in that future.
Devil Summoner started out as a what if. In the first Devil Summoner (I know it was released on the Sega Saturn), it's presumed you killed Thorman, stopped the ICBMs, and prevented the apocalypse. Devil Summoner 2: Soul Hackers (Saturn, Playstation) is the sequel. Where Shin Megami Tensei has you battling God, Devil Summoner had its main foe be Sid Davis and Soul Hackers' main villains were Sid Davis' Phantom Society. I don't know much about the first Devil Summoner game ('cept that it was often cheap), but Soul Hackers was cool. It was very cyberpunk.
Devil Summoner: Raidou Kuzunoha vs. the Soulless Army is the start of a new arc that takes place in an alternate version of the 1930s Japan (Taisho era 20), so it too is a "what if" the Taisho era had continued past Taisho 15. King Abaddon is the next installment of the Raidou Kuzunoha arc. (Kuzunoha is definitely a nod to Persona 2: Innocent Sin/Eternal Punishment since it prominently featured the Kuzunoha detective agency as rumor-spreading central.) The Raidou Kuzunoha games are the only Devil Summoner games to be released in the US. Atlus tried to localize the Playstation version Soul Hackers, but were denied by Sony (or so that's how the story goes.)
Gameplay-wise, the Devil Summoner games added demon loyalty to the mix. If you didn't do well by your demons, they'd be disloyal to you and either disobey you in battle, turn on you, etc. In Devil Summoner (Saturn) demons were said to get disloyal pretty quickly. Soul Hackers was much better about that.