Fragmentation is when an organism is split into fragments, and each fragment grows into complete, individual organisms that are clones of the original organism.
Regeneration is the process of regrowth that organisms that allows for partial or complete regrowth of tissue after a damaging event.
The difference is that fragmentation specifies two parts each growing into complete organisms, but regeneration is simply a general process of regrowth. Few species are capable of fragmentation, but ALL species undergo regeneration, to varying degrees.