It looks like you're discussing the formation of coral reefs and their surrounding areas as an island sinks. Here is a comprehensive way to fill in the blanks with appropriate terms related to coral reef ecosystems:
As the corals grow, they form a fringing reef around the island. As the island sinks underwater due to the weight of the coral and rock, the coral reef area expands. Eventually, a wide band of water called a lagoon forms between the reef and the island. The fringing reef has become a barrier reef. Any corals that rise above the ocean’s surface form cays, and their skeletons create sand and rocks mixed with coral and algae. Now a coral reef surrounds the central lagoon, changing into an atoll. New coral reefs forming inside the lagoon are called patch reefs.
This terminology reflects the stages in coral reef development and the transition of habitats as geological and ecological processes occur.