Exactly right, Deep rough is intermediate between recovery and rough. If you have to punch out from trees, that is a recovery shot, or if you have to hit a wedge out of deep fescue, that is also considered a recovery shot. Deep rough is typically an unobstructed shot but deep enough that you can’t hit the normal club that you would from the rough and probably can advance it further that a recovery shot be can’t reach the green.
Deep rough is intended to give the ‘appropriate’ cost allocation to the previous shot versus the recovery / deep rough / rough next shot.