Anything that makes the vocal cords uneven (in mass, length or tension) can put them out of sync. With a mild asymmetry, they may oscillate out of phase. Under a strobe light, it will look like they are chasing each other. They may never touch each other and so effectively, even while they are crossing each other’s path in the midline, they do so at separate times, so air continuously leaks out. This is a gap created by timing.
The same vocal cords viewed at two moments in time. In the left photo, the right vocal cord is near the midline and the left vocal cord is at its apogee laterally. In the right photo, the left cord has now come to the midline, but the right cord is now out in a lateral position so there is always an opening allowing continuous air leak.
If they become slightly more asymmetric, they may begin to oscillate at different frequencies. Two pitches are created simultaneously – diplophonia. The separate frequencies are perceived as roughness. And in this case we would actually hear both huskiness and roughness. The huskiness is from the gap. The concept of roughness brings up the other type of hoarseness: roughness due to vocal cord asymmetry.