I tend towards this explanation from Charles & Linda Raabe.
" Besides acting as a major component of our filtration, Live rock, Base rock and sand also provides our tanks with some diversity of life forms. For the sake of using correct terminology, Live rock is NOT bare rock that has some filtering bacteria on it, I don't care who or how many people continue to use the term "live" for what should be correctly called base rock. To state that a base rock is "alive" just because it has had time in a tank to develop some bacteria on it is misleading, if that was the case, then I have "live" glass, and "live" plastic in my tank. As the filtering bacteria will grow on anything you put in the water. LIVE ROCK = rock that has been colonized by a multitude of life forms including, but not limited to: corals, sponges, algae, inverts, worms and of course bacteria which forms a habitat unto its own. This type of habitat forms the foundation of all tropical reefs.