I think client is someone who seeks a professional like a lawyer. We call them clients, there is usually a relationship between the professional and the client, especially in business relations. Customer is more like someone who purchases goods and services. So if you go to a restaurant you are a customer who is buying food and paying for the hospitality. There can be overlap name between the two and sometimes they are interchangeable as with strange and weird. But there are some subtle differences. You use client for when a person seeks a professional or has a business relationship. A consumer is a more broad term than the other two. It describes what people are in a free market capitalist economy where we consume goods and services, different products, and also advertising and entertainments. Even when you walk down the street and you see advertisements, you are consuming them in that you are taking it in and it affects your purchasing decisions. The word consumer can be used to describe both a client and a customer.