This is just a rant because it bugs me that people use Dual layer and double layer interchangably. Double layer drives are available now. They're DVD+R DL. Dual layer is DVD-R DL. As far as I know there are no Dual layer drives available, though interestingly enough there may be a dual-layer rewritable drive soon. (DVD-RW DL) JVC has announced that they plan to send engineering samples to the DVD Forum for approval.
The Pioneer DVR-109 now supports DVD-R DL disks, although I confess that I was one of the ignorant regarding the nomenclature you bring up. http://www.pioneeraus.com.au/computer/dvdwriters/dvr109/
Do you honestly think it matters? Even if your distinction is accurate, there's no way, in common communication, that people are going to keep it straight. Using dual vs double doesn't add or detract from the information being conveyed, i.e. it's a useless distinction. It's basically a happy vs glad thing. Pick one. If you want to be pedantic, fine, but you'll find yourself in a very small, ignored minority.
The terminology is indistinct. The +R, -R is something that still needs to be a descriptor. The organizations that have created these terms have used them semi-interchangeably. The term dual and double can precede a +R or +RW disk (as noted in the press releases above, also see the same source for white papers). I see the same for -R, -RW, so regardless people still have to specificly the kind of media they need, including the +/-. If it was really ment as a delination, then the terms should not be so simular, or as interchangable.
I didn't say a thing about +R or -R, did I? That's the only distinction that counts. Use double or dual as you please.
From an article re: a Sony drive. Double Layer vs. Dual Layer There are currently two formats on the market that support recording to two layers of a DVD disc. The first was presented by the DVD+RW Alliance for the plus ("+") format and given the formal name "Double Layer." The DVD Forum followed with its own standard for the dash format ("-"), which it dubbed "Dual Layer." For now, drives are only available in write-once formats called DVD+R DL and DVD-R DL.