Technically-speaking, aquacultured coral is grown in a closed system, and maricultured coral is grown in an open system. The closed system is very much like a saltwater aquarium, but one that is highly specialized to promote the growth of whichever coral species is being cultured. The open system is generally the ocean, where the coral is cultured in a protected lagoon.
Where the distinction is made, maricultured coral is generally slightly less expensive than aquacultured coral because aquacultured coral is commonly, although sometimes erroneously, thought to be hardier and less prone to carrying diseases and parasites. The reason that aquacultured coral is considered hardier is because it is raised in captive conditions (e.g., artificial light, captive water conditions, etc,). Aquacultured coral therefore does not have to be acclimated to captive conditions in the same way that maricultured coral does. As such, aquacultured coral may make the transition into the hobbyist’s tank better, although they tend to be somewhat more expensive than maricultured corals.