This is a choice, a huge one in the life of the freelancer, the entrepreneur or anyone who seeks to engage with the marketplace.
The customer buys (or doesn't buy) what you make.
The client asks you to make something.
The customer has the power to choose, but the client has the power to define, insist and spec.
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, though, and your work happens after you find them.
If a customer doesn't like what's on offer, she can come back tomorrow. If the client doesn't like what you deliver, she might leave forever.
You can do great work for either.
But don't confuse them.
Choose your customers. Choose your clients.
And most of all, choose which category you're serving.
[Worth noting: Software and the internet let us disrupt a market by transforming clients into customers and customers into clients. People who used to have to take what was an offer can now get a customized version almost as easily. And people who used to pay extra for the bespoke version can now have the convenience and economy of merely buying what's on offer.]