What are Mammals?
Mammals are warm-blooded living organisms belonging to class of higher vertebrates whose bodies are covered with hair, who give birth to live young ones, and feed them with milk from mammary glands.
What are Fish ?
Fish are mostly cold-blooded aquatic vertebrates that may or may not have scales, they breathe through their gills, and are equipped with two sets of paired fins and several unpaired ones.
Is Shark a Mammal or Fish?
Breathing Mechanism of Marine Mammals
Marine mammals or sea mammals, like whales and dolphins, draw air into the lungs by breathing through the 'blowhole' (similar to nostrils in terrestrial mammals) on the top of their head. For this, they have to come to the surface at regular intervals. Once inside the waters these marine mammals close their blowhole and hold their breaths.
Breathing Mechanism of Fish
Fish have gills which help them breathe oxygen directly from water without any need to surface. The fish takes water through its mouth, pushing it over the gills and back out through the gill slits. The oxygen enters the blood vessels after being filtered by the gills. Sharks do not have lungs, but have between five and seven gill openings.
Fish have skin covered in (smooth or rough) scales. They are cold blooded, which means they cannot keep their body temperature steady, hence can change as per the climatic conditions of the water they are swimming in. Sharks have rough tooth-like scales covered by thousands of tiny teeth called 'dermal denticles' which not only protect their skin from parasitic damage, but also helps them move really fast in water.
Dorsal Fin of a Fish
Fish have more than one dorsal fin, and pelvic and/or anal fins too. Sharks, depending upon their species, have first, second, pectoral, pelvic, anal, and/or caudal fin which they use for stabilizing, steering, lifting, and for thrusting ahead. Shark fins do not allow them to swim backwards, hence, they can only drift away from objects directly in front of them, instead of moving sideways.
Once you are well-versed with the basic difference between mammals and fish, it becomes more than obvious that shark is a species of fish - not a mammal as many people believe it to be.