I’ve not used a diving dry suit, but from what I have heard from divers who do know the difference, they are not the same thing.
Seems diving dry suits are also a bit more tricky than paddling dry suits, as PADI has a special course on how to use them. Looks like the diving dry suit has some way to control the air inside the dry suit. https://www.padi.com/courses/dry-suit-diver
Zombie thread lives!!! 16 year thread revival 
Scuba divers who do not wear a diving dry suit wear a BCD, or buoyancy control device, which looks superficially like a PFD. It is hooked up to the air tank and can manually let air in and vent it to maintain neutral buoyancy. With a diving drysuit there is a similar system where the drysuit itself provides the neutral buoyancy, and is hooked up to the air tank and again. you can let air in and vent air out to maintain neutral buoyancy.
Buoyancy control is critical for safe diving. As you descend, a wetsuit or drysuit compresses and your buoyancy decreases. As you empty you air tank, your buoyancy increases. Your buoyancy also increases as your wetsuit expands. You want to have neutral buoyancy at working depth and you want to control your rates of ascent and descent.
A diving drysuit does not have to have a tighter neck gasket than a paddling drysuit, because, if used properly, the air pressure inside the suit will closely match the water pressure outside. Of course, in both cases you want the neck gasket tight enough to keep water out, and in the case of a diving drysuit, air in.