Corals each have different requirements as far as lighting and flow.
Mushrooms don't like alot of light so i put mine on the bottom under an overhang kinda. SPS on the other hand need high light so I place them higher up in my tank.
Some corals can spread onto rock like zooas, I have several I had on frag plugs and they have overtaken the plug and are now growing onto the rock the plug was on.
So, no, I don't think they root per se, they are almost always moveable by you.
You can check out the requirements for many corals here:
Saltwater Reef Aquariums: Live Coral for Saltwater Coral Reef Aquariums