No. A coral reef is just a reef made out of coral. There are many other kinds of reefs. A coral reef is just one kind. The Great Barrier Reef is a specific coral reef. There are many other coral reefs in the world.

The Great Barrier Reef is a coral reef.

in the coral reef in the coral reef

It does not rain in a coral reef because the wind near the coral reef is dry and has no moisture

A coral reef is an underwater ecosystem characterized by reef-building corals