A group of individuals or polyps that are attached are termed a colony. Note that in instances where areas of skeleton are attached but connecting tissue between polyps die, such as in Lobophyllia, (p. 6 of the Coral Finder), the term colony is still generally used. Colonial corals may also be termed modular.
Corals may live as a solitary polyp or clone to form a colony of many polyps. Solitary corals can be as large, or larger, than colonies. The genus Ctenactis (left) and Moseleya (right). Note: both of the corals illustrated are also free-living.
Free-living corals can be solitary or colonial - the genus Fungia (left) & Halomitra (right).