While they are directly connected, they are also complete stories. Innocent Sin is the original, so you can play it, and finish it, without needing Eternal Punishment. I wouldn't recommend playing Eternal Punishment without playing Innocent Sin, though.

That said, while the writing in the games is great, I don't really recommend the early Persona games. I don't feel they aged particularly well overall, and it wasn't until Persona 3 that I feel the series actually developed its own identity.