To further complicate matters, what today's Cat of the Day is wearing is called a mortarboard - but colloquially known as a graduation cap.

Hat and cap are somewhat interchangeable, but as Sara mentioned, a cap is generally less formal.

The Queen mum, for example, wore hats. Prince Charles often dons a cap.

And a baseball cap, when worn facing front, makes a great hands-free umbrella for one's eyeglasses!