Nerd warning. I went on a bit of a deep dive some time ago. I have no formal mineralogy training, so please point out any mistakes if you do see them.
The leopardstone Koetsu is made of "leopard skin jasper". Jasper and agate (as in blue lace agate) are both forms of chalcedony, which is a microcrystalline silica. The difference is that jasper is opaque, while agate is translucent.
Onyx (as in blood or white onyx) and agate are in turn both translucent and
banded - onyx has straighter bands, while they are curved in agate.
So,
- jasper = opaque chalcedony
- agate = curved bands in translucent layered chalcedony
- onyx = parallel bands in translucent layered chalcedony
In other words, for Koetsus,
Jaspers - leopardstone, blue azule, bloodstone models
Agates - blue lace model
Onyx - white onyx and red onyx models
Chalcedony not otherwise classified above - carnelian model
Other non chalcedony mineral types - jade, brown/blue tigers eye, rhodonite and coralstone models