Rays

Rays are close relatives of the sharks but they have significantly modified body shapes. Some are bat-like (the Batoids). Some are torpedo shaped (the Torpediniformes). This group includes the electric ray which can stun prey with an electric shock.  

Bony Fish

this is the largest grouping and includes most of the important types that are fished for food. Given the name, you will probably have guessed that the main characteristic is that they have a bony skeleton!  

Sturgeons and Paddlefishes

The Paddle fishes are an ancient group of fish. The American Paddlefish is sometimes called a ‘Spoonbill’ because of its distinctive mouth. It is a freshwater fish found mostly in the Mississippi and associated rivers and feeds by filtering zooplankton (tiny aquatic animals) from the water. This animal can be big at up to 65 kilograms.  

Reedfishes and Bichirs

Birhcirs are unusual fish that are popular pets for aquarium owners. In the wild, they are mostly found in rivers in Africa. They have simple lungs and can cope with water where there is not much dissolved oxygen (such as slow flowing, hot rivers or warm ponds).

Gars and Bowfins

Bowfins are found in the Great Lakes and are another ancient order of fish. They are more like modern fish than most other primitive species, though. They rear their young and they have scales rather than bony plates. More here:  

The Teleostei

Most fish living today (well over ninety percent) belong to this group. One of the chief characteristics of the Teleostei is that the fish can move their jaws forward (as well as up and down). If you ever watch a goldfish feeding you will understand what a big advantage this is. The jaws of a Teleost are capable of very precise movement and this helps locate and secure tricky foods.    

Jawless Fish

some very primitive kinds of fish- the Hagfish and Lampreys- still exist from the time before animals evolved jaws.        

Sharks

Sharks are a varied group of fish that evolved well before the Teleosti, described above. They are mostly predators, although, some, like the huge whale shark, are filter feeders. The popular image of sharks as dangerous killers is at least partly true. White Tip sharks are deep ocean dwellers that will attack anyone they find in the water. Great White Sharks will occassionally attack surfers and swimmers close to shore.