The Vuze client is just the new name for the Azureus bit-torrent client.  Starting with the 3.1 release, the client was renamed to "Vuze" but as far as the bit-torrent client is concerned the two are synonymous.  Vuze, Inc. is also the company that develops and supports the Vuze client application, and the Vuze HD Network is the marketplace for videos, music, and games -- most of it high-definition and most of it available for free -- available from Vuze, Inc.