Binge eating is consuming a huge number of calories at one sitting. I've seen it defined at 15,000 calories at a time. It generally takes the brain about 20 minutes to get the message that the stomach is full, so unless someone ate awfully fast, it would be difficult to take that many calories without at least some of them being eaten while not hungry.
Binge eating is not eating when you are not hungry necessarily but it is the uncontrollable eating episodes. It is eating that is disordered and is also known as compulsive overeating disorder. Read details at http://en.wikipedia.org/wiki/Binge_eating.
Binge eating is eating a LOT in one sitting/one serving. It's often accompanied by purging (vomiting) afterward, as in the eating disorder bulimia. Although, many people binge eat w/o purging. And, in a way.. Yes (to your Q)... it often happens when one is not hungry, or is no longer hungry, but keeps eating, anyway.