I find this topic very interesting. I've read some (by no means all!) of the posts, and one element of "Online Chess" that I haven't seen mentioned is the element of simultaneous play. We're all focusing (appropriately enough) on the time element, but for me another defining characteristic of Online Chess is that I typically have many games going at once.
I suppose it's possible that some people open more than one chess.com window and play simultaneous Live Chess games; but I doubt that this is a common practice. I think that most Live Chess players play one game at a time, whereas most Online Chess players play multiple games at a time.
How about "Simultaneous Chess," or "Simul Chess," for a different take on the naming problem?
Internet Radio Chess (IRC)