Shin Megami Tensei games involve some kind of world-ending scenario, and are focused on gameplay and philosophies of rebuilding the world rather than socializing with friends. Persona DOES pull from the same pool of monsters that Persona uses as Personas, save for a few that are made exclusively for Persona. They share a lot of mechanics in aspects like the combat and fusion, but SMT goes from dungeon to dungeon rather than having any kind of calendar or focus on making friends with people.
If you like the dungeon crawling of Persona 5 (as P3 and P4 are randomly generated dungeons), the combat, fusion, and the creature designs in Persona 5, you might like this game.