There are two distinct qualities of thread cutting taps (internal thread) and thread cutting dies (external thread). 

For traditional engineering, hard steel and stainless steel High Speed Steel products are used.
For thread restoration and generally working in non-ferrous (copper, brass, aluminium etc) metals Carbon Steel Products are used.

A hand tap is used to manually cut an internal thread. Normally, a hand tap set consists of three taps: taper tap, center tap and finishing tap. The hand taps have a square shaft (square according to DIN 10) to be clamped securely in thread holding tools. The hand taps can be clamped in an adjustable tap wrench or ratchet tap wrench.

A die is used in conjunction with a die stock and is used to cut an external thread.

Hexagon Die Nuts are no longer readily available although a lot of low quality carbon steel thread restoration "dies" are actually hexagonal in shape mirroring the traditional shape of Hexagon Dies Nuts.

It is always fully advisable to use some for of thread cutting lubricant, no matter what your project is. Thread cutting lubricant makes the whole process a lot easier and extend the life of taps and dies.