The Fan Coral at the left is striking, as it sways gently in the current. The vein structure is presumably just a fractal solution to providing flexible strength, and not for fluid flow. There are many other varieties of soft coral, some visible in the backgrounds of the fish pictures.
The Thin Leaf Lettuce Coral on the right is common off Belize, occasional in the rest of the Caribbean, and not reported off Florida.
The hard Branched Finger Coral on the left has soft coral protruding out of it.
The Brain Coral on the right has its coral polyps exposed, because I took the picture at night.
The Coral on the left provides an even better view of the coral polyps. During the day they hide for protection inside the hard calcium holes, but at night they extend outside.