The difference for me is control.
I can give you an example from my own life. Yesterday I overate (or at least in regards to my diet). I knew we'd probably either order food last night or go out to eat so I purposely ate less the whole day and didn't have any snacks. Between breakfast+lunch I ate ~800 calories (it would've been 100 less but DH put the wrong milk in my coffee in the morning). We went out to an all-you-can eat pizza place and I ate ~1200 calories there (I checked the website afterwards) so my total for the day was ~2000, which is slightly below maintenance level at this weight. I ate over my normal amount for the day but it was planned ahead and big workout is almost planned for today.
I also don't feel guilty afterwards because I'd rather do that once a week or every two weeks and lose slower (but still continue to lose).
However, binging is uncontrollable, unconscious eating. I've eaten an entire 170g bar of chocolate in the not so distant past. Total calories were over 900, it wasn't planned for and I probably ate normally that day so it put me WAY over average. I don't remember the exact situation (it was probably 1-2 months ago) but it was definitely an emotional response rather than hunger.