Basically there is no difference between these terms; the difference is only in terminology.
It depends upon the scope of the term.
Thus, a particular form of e-business is e-commerce. Compared with e-commerce, e-business is more generic term because it refers to not only information exchanges related to buying and selling, but also to servicing customers and collaborating with business partners.
More specifically, e-business enables companies to link their internal and external processes more efficiently and flexibly and better satisfy the needs of customers.
E-commerce includes online display of goods and services, order taking, billing, customer service and all handling of payment and transactions.
However key business processes such as Customer Relationship Management (CRM), Supply Chain Management (SCM) and Enterprise Resource Planning (ERP) is not a part of e-commerce.
E-business is broader term than e-commerce.
It is usually taken to mean the integration of electronic processes beyond buying and selling activities, e.g. full integration into organizations ERP systems or equivalent business tools to undertake business process by electronic communications end-to-end.