The first pic is Tubastrea, it will more than likely be happier in a shaded area of the tank or in a cave. They are non-photosynthetic and must be fed to survive, what's more is each polyp must be fed, those that do not feed will die. I've seen some Sun Corals that were kept out in the open in bright parts of the aquarium and still opened up, the vast majority of them I've seen happy were in shaded areas.