According to The Real Estate Wiki, a real estate customer is someone you work with who has not signed a legal agreement for your services.
A client is someone who has engaged your services as a Realtor® and has signed either a listing or a buyer-brokerage agreement.
In other words, a client in real estate has agreed to pay your commission and to respect the business arrangement described in the contract you both signed.
A customer is someone who is still looking around and deciding whether or not they want to use your services.
This distinguishment is found in all sectors of the marketplace, but maybe there are more than two levels.
For example, you could say there's the prospect, who is still deciding, the customer, who has decided to go with you but hasn't yet committed and the client, who has signed a listing agreement or contract with you or the brokerage for which you work.
What do you think?