Plywood can be classified in many ways, depending upon the wood used, uses, density, etc.
Broadly speaking there are two types of plywoods:

Industrial: This type of plywood is usually made from semi-hard or hard woods.  It is also called as construction plywood. IT is used where strength, stiffness and construction convenience are more important than appearance.

Shuttering plywood is an example of industrial plywood.

Decorative Plywood: Decorative plywood is also called as Panel plywood. It is made from many types of woods. Like the name suggests, decorative plywood is used where appearances are important - in furniture, wall panels and cabinet panels.

Apart from this broad categorization, there is some specialty plywood as well.

Marine Plywood: The best quality marine plywood is waterproof, and is used for shuttering. It can also be used for making high grade furniture. Used when moisture resistance is a priority.

Film faced plywood: This is a special kind of shuttering plywood. It can also be used for making furniture.

Aircraft Plywood: Made from mahogany or birch, this is a high-strength plywood specifically made for aircrafts. It provides increased resistance to humidity and heat.

Some other kinds of plywood types include hardboard, particle board, paneling, etc.