What Commerce is
In general it means to conduct transactions online. It is considered a technological term because any kind of commerce conducted online requires a technological application behind it. From a marketing point-of-view, commerce is discussed with reference to the three big C's: content, commerce, and community. These are thought to be the three components driving the new economy.
The meaning of E-business
Any business that is deriving revenue at least in part from something "electronic," usually on the Internet. It also refers to a strategy or service that enables a business to do more business because of Internet-related technology (see: Cisco, for example). The tendency for companies to put an "e" in front of a new product or service primarily comes from marketing departments that are trying to convince consumers they have an online strategy. The traditional brick-and-mortar firms that are starting an online component will use this marketing term to announce they are now online.