I've always assumed that the camp is in the same place that we've identified as a safe spot to sleep in the general area, and we trek back there each night.
In my gameplay if you Long Rest on the surface then yes, you teleport to same beach/island.
But Long Resting in dungeon's changes the graphics for, well, an enclosed area. Withers and Goblin Slayer with Scottish accent if you activated them teleport to it
