It depends also on what type of business. For example in Finance a consumer is a real person who buys/borrows uses something but a customer is a general term for a person, business, organisation or partnership that buys goods or services.

For example, I might have an account at XYZ Bank and so might a company. We are both customers of XYZ Bank but I am a consumer and the company isn’t.

[to complicate things small businesses might class as consumers in some jurisdictions]