According to the Louisiana Department of Wildlife and Fisheries Enforcement Division, the definition of a turtle trap is quite liberal, essentially calling it any device used to catch turtles.
One major requirement is that part of the trap be above the surface of the water. This is common sense, as turtles are air breathers and need to get to the surface to breath or they will drown.
This is one of the few pieces of gear besides hook and line that do not require a recreational gear license. A basic recreational fishing license is all that is required to use a turtle trap.