All depends on some terminology.
What is called "dead sand" in normally dry, purchased sand, hopefully collected from the sea and cleaned, dried, packaged and sold for the hobby.
"Live Sand" is basically the same stuff of very recent collection from either the ocean floor or collected and kept in holding vessles for aquaculture. Live sand contains bacteria only, and again is cleaned somewhat, but is packaged wet, and sold for the hobby.
A "Live Sandbed" is what a mature tank sandbed hopefully will become over time. The sandbed has the bacteria, and many small creatures, worms, mini brittlestars, amphipods, copepods, and other critters that live and populate the sandbed. Normally these critters come in on good live rock, and make their way into the sandbed, or they are purchased from suppliers individually or as part of a detritvoir kit.
Dead dry added sand will eventually become "live" with bacteria naturally, but to have a good variety of critters in a "live sandbed" you must add these critters to the tank.
HTH
Brian