Lets start with a scientific description :
The common name of that class of vertebrate animals which lives exclusively in water, breathes through gills, and whose limbs take the form of fins (see Ichthyology).
and lets have a look at some generic types and their anatomy now:
1. Bony Fishes (Osteichthyes)
Fish with bony skeletons. i.e. Lungfish, Trout, Bass, Salmon, Perch, Parrot Fish
1.1 Flat Fish
1.2 Round Fish
2. Cartilaginous fishes (Chondrichthyes)
The jawed fish with cartilaginous skeletons. i.e. Sharks, Rays, Rat-Fishes
2.1 Sharks
2.2 Skates and Rays
3. Agnatha
Primitive jawless fish. i.e. Lampreys and Hagfish
4. Others
4.1 Coelacanth
The coelacanths are the closest link between fish and the first frog type animals. Their fossil record goes back 400 million years. The modern species are predators and live in the deep ocean.
4.2 Oarfish
It is a strange looking fish and the longest bony fish in the sea. (Up to 17 meters) Lives is deep ocean between 300 meters and 1.000 meters. Known as “king of harrings” or “ribbon fish” as well.