Client vs. Customer
The terms are not interchangeable in Real Estate.
If you represent the seller, they are your client and their buyer is your customer. Inversely, if you represent the buyer, they are then your client and the seller is your customer. If you represent the seller and the buyer, they are both your client.
A client is for whom you are working and to whom you owe fiduciary duties. A customer is with whom you are working.