You can own corns in TN as long as you can document that they're captive bred-which you should get from your breeder (or the pet store) or if you get the animal from a rescue, from them (we have a rescue corn in TN-and she's actually a normal coloration, albeit not all that typical for normals in West TN). The same is true with other snakes which are native to the state.
Breeding/selling requires permits, but not just keeping them as pets. And I have that from TWRA non-game agents.
Turtles/tortoises are something completely different. My daughter found a shell of a box turtle while out herping with the TN Herp Society folks last September-and was told that she couldn't keep it because it was illegal to even have PART of a turtle in TN. Yet, every single pet store has turtle food, care supplies, etc, so obviously SOMEONE is keeping turtles as pets!