Agate is a variation of Chalcedony, which is a variation of silica that is called cryptocristalline. Cryptocrystalline means that the mineral crystals are so fine that they are only vaguely seen in patterns and fine variations. Chalcedony has the crystals quartz and monganite that are finely grown and intermixed with each other. In addition there may be other minerals that will lend color or provide certain qualities.
Chalcedony is found in all 50 states of the US and in igneous, metamorphic and sedimentary rock.
Agate is the banded and infinitely multicolored variation of Chalcedony, with so much variation that no two agates are alike. It forms in rounded nodules and knobs and is quite ugly in its natural state. But when sliced and polished, agate becomes something wonderful to behold. Agate is very brittle and can break with relative ease.
There will probably be no comprehensive list of all possible names for Agate, because old names number in the hundreds and new names are coined frequently, mostly with no involvement by scientists who go through the rigors of properly classifying the rocks. Additionally, some agates have two names assigned to the same type of agate. Plus, the non banded agate is actually a type of chalcedony, but might still be called agate, as with dendritic agate or dendritic agate (chalcedony).
There are agates with lacy or wavy bands, as with Blue Agate.
Sardonyx and Onyx are straight-parallel banded agates with Onyx offering the most straight and regular formations. To futher confuse matters, chalcedony is dyed black to make Black Onyx, since that color does not exist in nature.
Other banded agates are Snakeskin agate (concentric bands), Star agate (bands in the shape of a star). Brecciated agate has bits of agate that have somehow naturally been forced or cemented together.
Crazy lace agate has varicolored bands that have twisted or turned by some process.
Dendritic agate, sagenite agate, scenic agate and sweetwater agate are all chalcedony. Some have tree or fern fossils as inclusions. Scenic agate has tree like designs that resemble landscape scenes.
Cloud agate has blurred or foggy appearance in the markings.
Enhydritic or Endro agate has water contained inside the nodule that is visible when held up to light.
Eye agate has banded or concentric rings.
Fossil agate and pseudo agate happens when agate has replaced organic mater.
Iris agate and Rainbow agates have rainbow spectrums of colors when sliced thin.
Thunder eggs are nodules with agate inside and Tube Agate has tubular formations that can be hollow. There is a Fire agate that rivals Fire Opal in its qualities.