Consumer vs. Customer: is there a difference?

The answer is yes, if you ask me.  But to make things simple:

Consumer = Customer on a global level

Customer is a word that many people are much more comfortable with.  The difference, for these purposes, is that when I use the word customer, I am talking specifics.

A person can be a customer of a particular brand or business, but they cannot be a customer in general.  A consumer, is anyone who is a customer of any brand or business.  I am a Whole Foods customer, I am not a Netflix customer.  But I am, and will always be, a consumer.

As a marketer, I am trying to attract new customers from a worldwide (depending on the business) pool of consumers.