Actually, doctors have "patients", not "clients". People who have "clients" include surveyors, architects, lawyers, opticians, carpenters, taxi drivers, etc. A "client" tends to pay for a professional service, not a product. A "customer" tends to pay for a product, commodity, or a non-professional service, not a professional service. In many situations, the terms "customer" and "client" are used interchangeably. I would not call a taxi driver, for example, a person who provides a professional service, but taxi drivers routinely call the people they routinely serve "clients". A carpenter is not a professional, but I have heard them use "client" and "customer" when talking about their businesses. The local hardware store may call me a "customer", but the fancy store across the street may refer to me as a "client". A restaurant owner or store owner is apt to say "customer".
Confused? Good. That means you have been paying attention. Guidelines are fine (customers pay for products and non-professional services, and clients pay for professional services), but we cannot be deaf and blind to exceptions.