A customer buys goods or services from another person. A client seeks the professional knowledge and advice of a specialist, like a lawyer, accountant, real estate broker, etc. You sell to a customer but you serve a client. The relationship is usually short-term with a customer (like when you go the supermarket or the hardware store). With a client, you develop an ongoing business relationship.

client: someone who pays for the service of a professional person such as a doctor or lawer. (hospital/law office/...) customer: a person or company that buys goods or service. (supermarket/shopping centre/boutique/...) http://www.italki.com/answers/question/35054.htm#.USspQ-gb3bk