Have you ever watched your cat while he/she is purring? He purrs both when he exhales AND when he inhales. The purr is distinctive from other cat vocalizations. Other vocalizations such as the 'meow' are limited to the expiration of breath.
Per 'Everyday Mysteries' from the Library of Congress: A cat's laryngeal muscles open and close the glottis (the space between the vocal chords) resulting in the vocal chords separating and producing the purr sound. Studies show that the movement of the laryngeal muscles is triggered by a unique 'neural oscillator' in the cat's brain. A cat that has laryngeal paralysis cannot purr.