By design, in the real stall (with weight and balance within certified limits of course) the nose should drop forward
Most medium to high wing loading T-tail airplanes will do this only with the help of a stick pusher and/or ventral fins, an additional complexity to take into account when selecting a T-tail. This pitching moment sign reversal with fully deflected elevator normally takes place in the post stall regime though, that's why it is also called deep stall.
Anyway, imho, i think that the same term "deep stall" is used to define 2 different situations.
Exactly.
--M