By definition all e-commerce is part of e-business. Not all e-business is e-commerce.

Explanation:
If there is a direct financial transaction involved with the electronic process using Internet technologies it is e-commerce. If there is a non-financial transaction with an electronic process using Internet technologies it is e-business. Any transaction with an electronic process using Internet technologies is e-business. Therefore all e-commerce is e-business but not all e-business is e-commerce.

Examples:
Ordering a book on Amazon.com is e-commerce and e-business. Creating a map with directions from your home to the post office on Yahoo.com is e-business (no e-commerce involved).

Discussion:
There is a lot of confusion surrounding these terms. The confusion is not unlike that surrounding Marketing and Sales. Sales is part of Marketing. Marketing includes other activities, such as Advertising which is not Sales.

I hope this is clear. I get this question often.