There are four types of faucets used in homes today.
The first and most common type are Ball Faucets. These are the ones with a handle with a ball at the base which rotates around.
The second most common type are Disc Faucets. While a bit similar to the ball faucets, they can be identified by their cylindrical shaped body which allows you to rotate from side to side.
The third type is called Cartridge Faucets, identifiable by their handle which can be turned left or right, most of the time, to allow adjustments for water temperature.
The last type is the Compression Faucets. Some models may look similar to cartridge faucets but basically, a compression faucet have two handles which functions to let out water when loosened or less when tightened.