Hi Ibex,
Yes, I believe there is a difference between the two. I've examined numerous phragmites reed arrows in the Smithsonian, and the joints are noticeably different than the joints in Arundo donax. I once stopped in southern Illinois and cut some phragmites reed (at least that's what I thought it was) and was very disappointed in its weakness and flexibility. Of course it was green, so that may have made a difference, but it was so lightweight that there was no way I would have used them for serious arrows. I could actually just pinch the reed between my fingers and crush it flat! It also had bad kinks at the joints, so I eventually just threw it away.
I have driven thru central and southern CA and seen large stands of Arundo Donax along I-5, especially north of San Francisco. Arundo is far superior to the reed that I collected in southern Illinois. It is stronger, heavier, and straighter. I use it a lot, and have been very impressed with it. It makes great arrows.