Satan and Lucifer are one and the same however. Lucifer was just the name Satan had when he was still an angel of God. How does it work that the actual God is a villain though??
Actually, according to the Bible and Christian Theology, Satan and Lucifer are two different entities, however many people get this confused in modern times.
Lucifer is Latin for "bringer of light" who was God's brightest Angel who fell down from heaven for being too proud.
Satan however, has always been a demon who opposed God that lived in the Lowest circle of Hell and rules over all the demons. Satan is Christianity's equivalent to Hades.
I think the reason most people get them mixed up as the same one is because in John Milton's "Paradise Lost" they were the same being. However in Dante's "Divine Comedy" they're separate as they should be (I think... I gotta re-read that).
SMT is incredible, I thoroughly recommend you check it out. They span a few Genres but mostly stick to being RPGs of some sort. They began as Dungeon Crawler RPGs and are an interesting twist on the Monster Collection. What's cool about SMT is that they are generally open ended as you can align your character to different attributes usually 2 variations of the Good, Neutral and Evil, all of which have different endings. Your alignment also determines which Demons you can use.
Devil Survivor and Strange Journey on the DS are great entries. The former is an SRPG spinoff series, and the latter a dungeon crawler that sticks to the main canon. The Persona series is another spin off of the main series.
The monster desings are really cool and creative and you get to partner up with famous deities such as Thor, Amaterasu, and even Lucifer and such. If you like Pokemon, you'll likely like SMT.
What I'm curious about is how Fire Emblem is gonna mesh with it, I wanna see Atlus work with that. I have faith they'll do a great job.