UK
The Tap & Die Co lists (taper, second, bottoming/plug)
USA
McMaster Carr shows the following:
Taper ChamferHas 7 to 10 chamfered threads. Use for starting threads and in through holes. Requires less torque than other chamfers.
Plug ChamferHas 3 to 5 chamfered threads. Use in through holes as well as in blind holes that have sufficient space at the bottom for chips to accumulate.
Bottoming ChamferHas 1 to 2 chamfered threads. Variations of the bottoming chamfer include semi-bottoming, which has 2 to 2 1/2 chamfered threads, and modified bottoming, which has 2 1/2 to 4 chamfered threads. Use in blind holes where threads must come as close to the hole's bottom as possible.
Victor Machinery Exchange, Inc. shows the following:
Taper tap: 5-6 lead threads ground. The easiest tap for starting to thread a hole.
Plug tap: 3-4 lead threads ground. The most common tap: a "middle ground" tap for threading.
Bottoming tap: 1-2 lead threads ground. Used for continuing to thread a blind hole close to the bottom of the hole. It's difficult to start threading a hole with this tap.