Been there several times and it's one of my favorite parks. Fairview and Devil's step are the same park and no you don't have to go to the main park to register BUT, it is gated. If you arrive after 10pm then you need the code for the gate. Call the main park and talk to them about your plans and arrival time.
Now, the main park is the older original state park. It's sites are smaller so if you have a rig that is say 24 ft size then the sites are fine. Fairview has the larger sites and most will accomodate the big rigs. If this is just for an over night understand that either park is not convenient to get to. You need to want to go there. Both are on a 2 lane country road and it's pitch black out there when the sun goes down.
Fairview is where we stay when we visit the Jack Daniel distillery. If you have the time I suggest you stay a few days and take the distillery tour and have a meal at Mary Bobo's. Visit Lynchburg and wander the town, it's small and you can walk it easily. It's the best distillery tour there is and interesting too.