In the good old days, business was pretty simple. I had a cow, you had some potatoes. We showed up at the market and haggled. Nowadays we do not have to show up at market, and we don't even need physical goods or currency to conduct business.
Electronic business is the most recent step in the evolution of business transactions.
At Trethowans we prefer the term e-Business. Electronic commerce, or e-commerce, is a very broad term. E-commerce conducted between businesses differs from that carried out between a business and its consumers. Consumers find what they like, type in their credit card number and unpack the books a few days later. For a comprehensive view see article from Chicago University.