To the end user the functionality is intended to be the same. That is, traditional automatics (with torque converter) and Dual Clutch Automatics, both change gears automatically. To people who don't know or care about car mechanics there are only 2 categories, you either have a manual or automatic.

There needs to probably be a distinction between the car and the gearbox. The gearbox is a manual, add on the mechatronic unit (seperate part of the car that controls the clutches) and the car is an automatic.

Considering it is both Automatic and Manual (depending on how you look at it), referring to it as either you will be correct and incorrect at the same time. It probably needs a category of it's on. Dual-Clutch Automatic is too much of a mouthful