doubled vs double
Double does, and always has meant two ropes.
Doubled is where the confusion comes in.
There's an article in the November TCIA on dual ascenders. A dual ascender allows you SRT (just use one side, the other goes empty), doubled static (both sides contain rope, both sides get used) or doubled dynamic (both sides contain rope, one side gets used)
For arbo traditionalists you're always on doubled dynamic (DdRT). This is your steady girlfriend. SRT may be a fleeting thought like that really hot chick who you can't get up the nerve to talk to. Static doubled (DbRT) or twin line is the hot newscaster whose image you can only look at from a TV.
That was about as stupid an analogy as one could come up with.
The point being, if you hang with one system, it really doesn't much matter what the others are called because they're not even part of your reality.
However, if you're using a tool like dual ascenders you can be in and out of all three of the described systems, depending on the particular tree, and whatever mood you happen to be in at the time, or what system would best facilitate the tasks just ahead.