Actually a retread is just replacing the tread by gluing it on hence retreading where as a remould is put back into a mould and the tyre is heat formed again hence the remould but your right they all get called the same by the time the get to the end user...
Sorry you are wrong with this. That was taken from a google of search for what was the difference. they all get heat molded together then tread is put on.
The old retread where as you say glued the tread on and then baked is no longer.
If you got time do a google and they explain it very well