Renegeration is the growing back of a lost part of the body of an organism. Fragmentation is breaking up of the organism into smaller pieces upon maturation. These pieces or fragments grow into new individuals.
Regeneration is usually used as a method of defence whereas fragmentation is a mode of asexual reproduction.
Regeneration is mainly associated with the animals whereas fragmentation is mainly associated with the plants.
In regeneration, either a part of the body that is broken off or cut or the entire body can be regenerated. Example of regeneration of part of the body - Lizards cast off their tails to escape predators and then regenerate them. Regeneration of complete body is seen in small invertebrates such as Planaria and Hydra.
In fragmentation, an organism is split into fragments and the splitting may or may not be intentional. Each of these fragments develop into mature, fully grown individuals that are a clone of the original organism. It is most commonly seen in some algae.