Fragmentation occurs in multi-cellular organisms with relatively simple body organisation. Regeneration occurs in several fully differentiated organisms.
Fragmentation is a mode of reproduction. However, regeneration is not the same as reproduction, since most organisms would not normally depend on being cut up to be able to reproduce.
In fragmentation, the organism simply breaks up into smaller pieces upon maturation. These pieces or fragments grow into new individuals. In regeneration, if the individual is somehow cut or broken up into many pieces, many of these pieces grow into separate individuals.
Fragmentation results in complete reproduction. In regeneration, the entire organism can regenerate as in certain animals like Planaria, but mostly the organism regenerates only a part of the body. Example - Crabs can regenerate severed legs. Mammals can regenerate liver cells and blood cells. Lizards can regenerate their tail
Regeneration is carried out by specialised cells. These cells proliferate and make large numbers of cells. From this mass of cells, different cells undergo changes to become various cell types and tissues.