This is the key difference in a taper (first), plug (second) and bottom (third) tap.
The taper tap (1st tap) starts forming the threads and is the least aggressive, meaning the more delicate the material is the less stress is caused and also the more work needed.
The plug tap (2nd tap) is designed to make plugs, nuts and similar items. Short sections that is threaded from end to end. This tap is the most common tap in use. It provides a trade off between delicate/difficult materials and aggressiveness.
The bottom tap (3rd tap, final tap), also called a blind hole tap, is designed to reach the bottom corner of the hole and provide the most threads possible. Otherwise as you get towards the end of the threading it will get hard to turn and cause problems.
There are a hefty number of types of bottom taps, i.e. semi-modified bottom tap for specific needs.