Did you know that coral are actually animals?  They are heterotrophic (they can't produce their own food) and they are multicellular.  Those are the requirements for animals, and coral matches both of them.  Actually, there are a lot of animals that look like plants, and you might think you know they are plants, but they are animals.  Especially in the ocean.  There are lots of animals that look like seaweed or some kind of plant, but that is how it's supposed to look- for camouflage.