Agree that having names for each of the varieties would make it easier to discuss.
I'm not fond of using the term "pegged sidechain" but that is what the Blockstream folks call them now.
I don't think a "peg" is a good thing. Currency pegs have horrible implications, almost always fail, and I think calling them this brings them down, but I didn't choose the name.
If it was mine to name, I might have gone with "coin wrappers" or something without all the bad historical connotations.
I'd suggest 'lock' instead of 'peg'. 'Peg' brings up images of a cribbage board where pegs are moved around as needed, and that is also the failure mode of many currency peg schemes (I imagine.)
'Lock' is more indicative of what is happening here. BTC are locked with high security to back a sidechain extension. As always, the security is a function of the quality of the implementation of course, but it's pretty clear to me that quality in implementation will bubble to the top (very much unlike the opaque world of off-chain extensions that we have seen to date.)
They are correctly "freeze-locked" coins