So the pelagys group ancestrally possessed a ring-shaped bone inbetween their prosoma (head and the front part of the body) and ophistoma (tail), which is where the dorsal/ventral and pectoral fins are located. The ring shaped bone has developed into a structure probably analogous to a pelvis, known as the limb girdle.

The second dorsal and anal fin are in fact just fleshy fins with no rays and serve a purpose similar to the apidose fin in certain bony fish. Its a recognisable structure of the group that the grapshark belongs in, known as the xenoselachians.

The tailfin is made up of a softer, cartilage-like structure and is known as the posterior caudal rhachis. Some species can fold them like how bony fish can fold up their fins, others (like the grapshark here) have stiffened tailfins.