Many predators, as common sense will tell you, are streamlined and have a pointed head. So they can swim fast and catch their prey. This particular type of predator is what is called a rover-predator. Other predators like to ambush their prey. They are torpedo shaped and have big mouths so they can dart out from their hiding place and capture their prey.
Some fish have small bodies with upward turned mouths and flat heads.
Deep-bodied fish are flat from side to side, which helps them with maneuverability. It's like having armor. Fins are used for a number of things. Rover-predators have paired fins which are separated widely and are located low on the body for stability. Other fish have these fins higher on the body and have them oriented more vertically, to give a higher degree of maneuverability.