Many animals have confusing common names: polecats are not cats, jellyfish are not fish, and sea cows are not cows. The dolphin fish is another animal with a confusing name. Dolphin fish have only the most superficial resemblance to dolphins, to which they are not remotely related. With a bit of background knowledge and some common sense, they are easy to tell apart.
About Dolphins and Dolphin Fish
Dolphins are marine mammals, specifically odontocete cetaceans. This means they are toothed members of the whale family. Since they are mammals, dolphins have live births, breath air and control the temperature of their blood (this is called being "warm blooded" or an endotherm). Dolphin fish (also called mahi-mahi) are bony fish. Because of this, they reproduce by laying eggs, breath water and cannot control their body temperature well (so they are cold-blooded or exothermic).
At a glance
Dolphin fish and dolphins have only the most superficial similarities. Most dolphins have a pronounced beak-like mouth that projects from the face. Dolphin fish have a much smaller "beak." Dolphins have fewer fins: they only have a tail fin, a dorsal or back fin and two flippers. Dolphin fish have a tail fin, two ventral fins (below the flippers), pectoral fins (flippers), a dorsal fin and an anal fin.
There are other differences that may not be readily apparent. For one, dolphins have a blowhole (a modified nose) on the top of their heads. This helps them breath at the water's surface. Dolphin fish have a gill cover, which allows them to move water over their gills. Also, both animals have distinct fins. Dolphins have horizontal tails and dolphin fish have vertical ones. A dolphin's dorsal fin is shaped like a wave, while dolphin fish have sail-shaped fins. Dolphins also have fleshier fins.
Dolphin fish and dolphins do have some things in common. Both are adapted for fast swimming in the open ocean. As a result, both have streamlined bodies. The shape of a dolphin fish slightly resembles a dolphin mammal, in that it has a bulging forehead and a slight beak. Also, the colors on a dolphin fish can resemble certain porpoises.