Kingdom: Fungi
Division: Basidiomycota
Class: Agaricomycetes
Order: Agaricales
Family: Agaricaceae
Genus: Coprinus
Previously, Coprinus was a large genus that included all ink cap mushrooms. However, in 2001 genetic analysis found that these mushrooms are not as closely related as one would would assume from their appearance, and three new genera were created in the family Psathyrellaceae: Coprinellus, Coprinopsis, and Parasola. Coprinus comatus is the type species of Coprinus, so they and their nearest relatives kept the name. The common name 'Ink cap' may refer to any of these fungi, and they may be referred to in scientific terminology as coprinoid fungi.
Not all of the Psathyrellaceae are coprinoid fungi, however; coprinoid refers to these species habit of digesting their mushrooms, turning them into black mush. Some of these can actually be used as ink, while others are just inky in color. The self-digestion helps flip the cap inside-out, fully exposing the gills for quick dispersal.
Coprinus now consists of Coprinus comatus, commonly known as the shaggy ink cap (UK), shaggy mane (USA), or lawyer's wig mushroom (both); Coprinus sterquilinus, the midden ink cap; and Coprinus calyptratus, Coprinus xerophilus, and Coprinus spadiceisporus, which have not yet given a common name.
This rearrangement moves Coprinus from the center of a cloud of popular factoids to the edge; the common inkcap or tippler's bane (was Coprinus atramentarius, now Coprinopsis atramentaria) is famous for being poisonous if eaten when drinking alcohol, but is no longer a Coprinus. Coprinus comatus, which produces a usable ink, is. Coprinus comatus is, incidentally, also the one that you can eat if you catch it before it dissolves.