Members of the order Zoanthiniaria are commonly called Zoanthids, or Zoos for short. They are not typically considered to be classified as a true coral.
Zoanthids are the type organism that you either love in a reef tank, or you hate. The reason is, they can often be considered a pest and undesirable as they can sting and out compete (i.e. kill, smother etc) many corals. And as can be seen by some of the images below, they can be very colourful, making them desirable for others. It is generally recommended zoanthids are kept in a dedicated aquarium or with other mixed corals, and away from a dedicated SPS tank.
- Zoanthids: Coral? Anemone? Both? Neither? by Eric Borneman - Aquarium.Net
- Taxonomy in Aquarium Corals: Part 3 - Everything Else - Soft Corals, Zoanthids, and Corallimorpharians by Eric Borneman - Reefkeeping Magazine
- Zoanthids: Polyps as cute as a button by Julian Sprung - Advanced Aquarist's Online Magazine