Hoarseness technically is an impairment of the signal-to-noise ratio of the human voice, yet a more descriptive definition might be more helpful. I define hoarseness as the unwanted leak of air though the vocal cords or the irregular leak of air through the vocal cords.
Air leak and diplophonia
All hoarseness can be described in these two ways. In the first, the vocal cords do not come together as they should, allowing air leak. Let’s call this husky hoarseness. The second type of hoarseness is caused by asymmetric vibration. Because there are two vocal cords, when they are not symmetric, they tend to vibrate at two different pitches. A physician would call this sound diplophonia. Di- meaning "two" and -phonia meaning "voice", so two voices can be heard at once. Usually, since the vocal cords are only slightly out of sync, the diplophonia will be inharmonious and the perception will be of a rough or gravelly quality. We will call this rough hoarseness.
Simply put, there are only two ways to be hoarse.
Air is leaking when you don’t want it to leak. This is called husky hoarseness
The vocal cords are vibrating irregularly. This is called rough hoarseness