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A customer is a person who buys product, however a consumer is person who uses business products like services etc.
I'm not sure that there is one. But you could say that the customer is the person who buys, and the consumer is the person who uses.
Examples might include a newspaper bought by one customer but read by several, or children's clothes, or experience day gift cards, or a wife who routinely buys her husband's underwear. (Please excuse the gender stereotyping - it does happen.)
Most of the time they are the same person of course.