A contact is anyone with a profile in Ometria, regardless of their lifecycle status, or whether or not they are subscribed.

A customer is a contact who has placed at least one order.  

Example:

Julie has subscribed to receive marketing communications from you, and her email address is in your database, but she hasn't bought anything from you yet. Julie is a contact.

When Julie places an order with you, whether valid or invalid, she becomes a customer as well as a contact