Customer: A “customer” is someone who pays in exchange for a product or service. Example: Working at the mall was really difficult because I had to deal with rude customers.
Client: A “client” is similar to a customer, but we use “client” for professional services and when there is a longer relationship between the buyer and seller. For example, a lawyer has clients, but a convenience store has “customers.”
Example: When he started selling insurance, it was difficult to find clients.