Common Plane Styles

Smooth Plane - typically 8" to 10" in length and is primarily used for final finishing
Jack Plane - typically 10" to 14" in length
Jointer Plane - typically 14" to 24" or longer in length and is used for flattening stock and for edge straightening
Scrub Plane - usually about 9" in length with a wide mouth and a curved blade cutter. Primarily used as a first step to get rough cut stock ready for flattening.
Miter Plane - typically 8" to 10" or longer plane with the sides square to the bottom. Primarily used on it side in combination with a shooting board for flattening sides of boards.
Speciality Plane - the list is pretty much endless and may include: moulding planes, tong & groove, dado, block, router, dovetail, and many more. For a great description of the metal planes see Patrick Leach's 'Blood & Gore' There are many more good descriptions on the web if you wish to search for them.