The double D, most likely means double reed. Which means you have 2 layers of latex set into the frame of the call.
You're right, there are many different diaphram calls out there, differences b/t the calls are more plentiful they can be different stretches on the latex, different frame sizes, different latex and thickness of latex, many many combinations of numbers of reeds and cuts in the reeds to produce different pitches and rasp. Hate to say the list is endless. . . but there are alot of options to choose from.