Crystals

Crystals (also sometimes translated or referred to as gems, magic stones, demon stones, and cores) are a crystallized source of power residing within monsters. Destroying them means killing the monster. In the web novel and light novel, animals do not have crystals. The stronger the monster, the better the crystal, and the more crystal points it gives to Teacher.

When absorbed
So far, Teacher is the only one capable of absorbing crystals, and therefore the only one able to taste them. Rather than different flavors, it is more akin to the quality of magic deciding the taste.

Demonkin
The crystals of the demonkin have a vaguely spicy taste.