Morphollaxis: Very "primitive" single-celled and colonial animals do not have a lot of tissue differentiation - or none at all - no tissues. Beasties in this category can rebuild the whole 'body' because the position effect required for stem cells does not need to be extant.
Epimorphosis: found in more complex beasties like salamanders. They cannot rebuild the whole body with all of the tissues because that would require "reverting to a fertilized egg" (not real, never happens, just a phrase to help get the concept), so they are stuck perform much more limited repairs.
Both of these responses are a survival strategy. Lose a tail to a predator? okay, no big deal I can grow a new one. Better than the predator eating all of me. Same concept applies in both cases. It can be viewed as a return to homeostasis. That is the "place" where living things do best.
BTW: this stuff was old when I was young, which makes it really old. That is not inherently bad, it is just that 19th century biologists were driven to name things so they could put whatever they found into a cubby hole. Then say, 'See we know what this is all about because it has a name'. People have done this forever - if you can apply a name to something - classify it - then you are off the hook for really understanding the phenomenon. Or even thinking about it maybe.
You seem to have knack for digging this stuff up. A freshly minted PhD would probably wonder where all these oddball terms came from unless they took a History of Science class in their field. It was a required class for me 50+ years ago.