How do you view and hence refer to the people who buy your software or services? As Customers or Clients?
While it sounds like a simple case of semantics, it is a significant change in how you look upon them and how you treat them.
To explain the difference, consider the following analogy.
We refer to the doctor, lawyer and accountant we use as "My Doctor", "My Lawyer" and "My Accountant" but we never refer to the shopping centre we go to as "My Shopping centre" . It's referred to as "The Shopping Centre".
A customer is someone who you don't build a relationship with. You don't necessarily gain repeat business with. They are someone who can easily switch to a different product (shopping centre)
With the subtle shift to considering them as Clients, you are focussed more on working with them, finding solutions to their problems and gaining their appreciation and repeat business.