I have to say that I honestly don't struggle with the difference between them. I know when I'm making a conscious decision to eat something that is calorie heavy and nutritionally not-so-great. I believe that I really do have a handle on my lifestyle, which includes treats and no-count meals.
I will admit that I do struggle, once in a while, with what you describe as "sick" eating. That "oh well, I've f'd up so I might as well eat a whole bag of chips" kind of eating.
But I honestly - after 2 years of living like this - don't believe that the 1st leads to the 2nd for me. For me, the circumstances, conditions, and mindset that leads to the 2nd, the "sick eating" is WAY different from the first. I've never had a no count meal or a treat where I used it as a stepping off point for a binge, that I can recall.
For me it's 100% emotional - when something happens that really upsets my equilibrium, I abdicate from being responsible for my life and the first thing I turn to is food and drink. I know I'm doing it ... I don't deny it or justify it. I just do it.
Thank goodness it doesn't happen often and I'm learning to recognize the situations where it might happen and figure out ways to control myself that don't require me to have will power at that particular point. I'm also learning to better control my environment, my emotions, and have taken steps to change things in my life that have been affecting me emotionally and causing that kind of eating. I won't at all claim to be perfect at it, but I'm getting better ... slowly.