From Wikipedia:

While business refers to the value-creating activities of an organization for profit, commerce means the whole system of an economy that constitutes an environment for business. The system includes legal, economic, political, social, cultural, and technological systems that are in operation in any country. Thus, commerce is a system or an environment that affects the business prospects of an economy or a nation-state. We can also define it as a second component of business which includes all activities, functions and institutions involved in transferring goods from producers to consumers.