A customer is someone who buys what you make.
A client is someone who asks you to make something.
Both have the power to choose, but the client has the power to define.
There is a large number of potential customers, and you make for them before you know precisely who they are.
There are just a relative handful of clients you could handle, though, and your work happens after you find them or they find you.
You can do great work for either.
But don't confuse them.