Basic drain augers come in varying lengths and diameters. Augers with smaller diameters are used on internal drain pipes and larger augers are used to unblock external pipes.
Basic augers are not so much an actual type, but the main part of all the types of auger. They can be purchased as inserts or replacements for some of the other types of auger, such as drum augers or power drum augers.
A urinal auger is the same as a closet auger, only smaller. It is solely for unblocking urinals.
A drum auger contains the snake within a drum which is rotated by a handle. There are drum augers of various sizes which are for different applications including, in toilets, sinks, internal and external drain pipes.
Power drum augers are the same as drum augers but have a built-in power drill for rotating the snake. They also come in varying sizes for different applications, however power drum augers are generally used for heavy duty tasks as they are a more professional tool.