For a long time coral were a mystery. They were called a plantanimal, animal plant, and rock plant. We now know that coral are a complex mix of animal and plant life with microscopic forms of plants called algae living within the coral. The type of algae that lives within the coral are called zooxanthellae. The small animals that make up coral are called polyps. source
This video illustrates what happens when you drop anchor on a coral reef.