I think it is a mistake to try to refer to all bents by one name -- this is not done with DF's.
The only people who refer to DF's are bent riders or people who are comparing them to bents. No one says "diamond frame (or safety) bike for sale". They call it a mountain bike, a racing bike, a cross bike, a cruiser, etc. The bike is referred to by what it is good for.
Just as people ride DF's for different reasons, they ride bents for different reasons. I have a different type of ride in mind when I go out on my tadpole trike than I do when I'm on my highracer. These bikes really don't have that much in common -- a highracer really has more in common with a racing bike than it does a with a trike.