As for the difference between Shin Megami Tensei and the modern incarnations of the Persona series, I'd put it like this: Shin Megami Tensei is what you'd get if you took a Persona game; drained it of all personality and style; threw any story and characterization in the shredder; and then set the game in a post-apocalyptic world. If I'm being too subtle here, I vehemently dislike the other Shin Megami Tensei games (having played SMT 4, Devil Summoner 2, and Digital Devil Saga).
The Persona games took the SMT battle system, and they added a great sense of "style" and attitude to the experience, along with a strong focus on story and character relationships. They threw away the whole "demon negotiation" aspect of typical SMT because it was stupid, and they streamlined the game's systems to make them more approachable and less-inclined to just annihilate the player (it is by far the most popular franchise Atlus owns). Whereas the SMT series focuses primarily on dungeon-crawling, the Persona games split the experience between managing your character's daily social life to min-max the battle experience and actual dungeon exploration. Frankly, there's also just a tonal difference between the franchises, with Persona having a more optimistic, upbeat tone compared to SMT's dark & stoic tone.