The drifting larval stage released by many stony corals after fertilization is called a planula.
In many scleractinian species, adult colonies release eggs and sperm into the sea, often in synchronized spawning events. Fertilization produces a microscopic planula: a ciliated, generally flattened larva that can swim or drift in the plankton. Brooding species may fertilize eggs internally and release planulae that are already more developed.
A planula does not remain a larva indefinitely. It uses currents and environmental signals to locate suitable habitat, often a hard surface associated with a reef. After settlement, it attaches, undergoes metamorphosis, and becomes a primary coral polyp. That first polyp can then reproduce asexually by budding, building a colony of genetically related polyps.
The alternative answers are larval stages associated mainly with other animal groups. Nauplius is typical of crustaceans, veliger is associated with many molluscs, and trochophore occurs in several marine invertebrate lineages. Planula is the characteristic cnidarian term, including for many corals.