A slightly loaded question in reality. Live really speaks to the bacteria that is established during a cycle and the nitrafication cycle.
Stores will call almost anything live, depending on the store. Petco as an example sells live rock which was man made and simply cycled.
I ordered all of my "live" rock online. By the time it arrives, there is basically nothing left alive even if it was alive in the ocean. This being said, a year after the cycle things have come out of the rock that came in on it, a chiton as an example.
Generally, you should always be wary of things called live rock when placing into an established tank. Always cycle new rock even if it is live to prevent deadly, and costly, mini cycles. Calling it live gives people the safe feeling that they can just throw it into the established tank and things be just fine, which is why live refers to the bacteria rather than the creatures that could live within.