Persona series, Digital Devil Saga series, Devil Survivor series, and Devil Summoner series.
And to make it extra confusing for people. Persona 4 is called Shin Megami Tensei: Persona 4, while the Golden version is just Persona 4 Golden (right when they decide not to add SMT to everything Megami Tensei related).
They’re all considered spin-offs taking place in their own universes even in Japan; it isn’t something Atlus of U.S. decided. Even the first Persona game was originally called Megami Ibunroku, denoting the series to be a side story to the Megami Tensei games. Considering Golden is an enhancement to the previous game and a love letter to fans, they probably didn’t feel the need to include the SMT title on it because fans would already know what it was. All of the spin offs draw from the same lore, much in the way the FF series does. The only thing that separates them is gameplay style and story.
Yes, but in Japan they don’t add the SMT title to non-SMT games. Only outside of Japan does that happen, especially NA releases. The only games with the SMT title added to it are the ones directly part of the SMT line (Shin Megami Tensei, Shin Megami Tensei II, etc.) and the side-stories (20XX, NINE, Strange Journey, etc.).
It’s actually very weird that they added SMT to the Persona franchise at all. The only thing in common they have are the demon designs (and the Jack Bros.), but the themes are a very different. The Devil Summoning Program doesn’t even show up in Persona, nor do the Terminals.