Most of the plases I go to in NC put your sandwich on a piece tissue like bakery or pastry shops use (but bigger). If you order fries, they are in a paper tray. This is if you eat in. If it's "to go" the fry tray is wrapped in the tissue and so is the sandwich.
If you buy a small tray of bbq, it's a (sort of) cardboard tray... half filled with BBQ, half slaw. To go gets wrapped in the tissue.
A BBQ plate moves you up to a cardboard plate. "To go" get you the std restaurant styrofoam container.
Hope this helps some.
"Of all the imaginary friends I've had, I don't think there was one that I didn't end up having to kill."
in seach of Umami