I suppose its not "pain" in the sense that whacking your thumb with a hammer is pain. But it IS your body telling you via severe discomfort that what you are doing is really stressing it and you can't keep it up indefinitely without damaging something. Where the "pain threshold" comes in is you ignoring those warning signals from your body and going ahead and damaging something (muscle fibers in your heart and legs as well as other things). Obviously you "damage" your body just enough so that it has to rebuild itself stronger and more efficient.
Anyway, I'm with you on the idea that "pain" isn't the best term for it, since it doesn't hurt like putting your hand on a boiler plate hurts. But whatever it is is very similar to pain, since it is your body making an attempt to dissuade you from continuing what you're doing. Put your hand on a boiler plate - OW that hurts, I think I'll take my hand off. Ride well above LT until you have lots of lactic acid in your legs - OW this isn't very comfortable, I really want to stop, but I won't yet.