Within the Cnidaria there are four major groups of animals:
(1) The Anthozoa including true corals, anemones and sea pens - nearly all the major cold-water coral species are anthozoans
(2) The Cubozoa, which are box jellies
(3) The Hydrozoa, with siphonophores, hydroids and fire corals
(4) The Scyphozoa, better known as jellyfish.
Cold-water corals belong to two groups, the Anthozoa and the Hydrozoa.
The Anthozoa includes colonial stony corals (Scleractinia), true soft corals (Octocorallia) and black corals (Antipatharia). The Hydrozoa includes the calcifying lace corals (Stylasteridae).