Live rock = from a tank or ocean and has bacteria and other living things on it (sponges, algae, coralline coral, coral, feather dusters, ect.)

Dry rock = calcium carbonate rock that is either of terrestrial origin, removed from a tank or ocean and allowed to dry (killing all of the above life) or it could also be man-made rock (mixture of concrete and aragonite, ceramic or possibly others materials I can't think of)

Base rock = low end live rock. Generally it looks like dry rock but has the bacteria and sometimes a few other living things established on it.

HTH,
Tom