Is it a binge if...

This type of behavior is treading a fine line. Just don't worry about it and move on. Perhaps become more flexible with your calories over the week so you don't feel the need for these occasions.

I think you need to ask yourself why you are so concerned with labelling it a binge or not. Binges are usually uncontrollable bouts of eating and eating and eating, being unable to stop until you are physically too stuffed to eat anything more. But we all sometimes eat too much and it's no big deal. It only becomes a problem when we suddenly start obsessing over it instead of just eating less the next day to compensate as we'll likely be less hungry. And if your reasons for overeating go beyond a party or just having a good time and enjoying yourself on occasion, then it's not calories you want to worry about but your relationship with food. And if you're eating to the point of discomfort you're putting a lot of stress on your digestive system so try intermittent fasting to give your digestive system a break.

"I feel disgusting"

Then yes, I would call it a 'binge' - eating an unusual amount of food at once and experiencing feelings of guilt/loss of control. If it's once in a while, it's pretty normal to have the occasional face-stuffing session. If it is on a regular basis and you're feeling guilty and awful about your intake very frequently, that's when you might have a problem. Either way, it's important to just log it and move on . Maybe fit an extra workout into your week if it makes you feel any better, but since this is fitting your weekly calories, it's important not to dwell on it and accept that we'll slip from time to time. Restricting as a result of a binge often leads to more problems, including more bingeing.

I guess I'm just curious. I DID just eat more than I needed, until I was stuffed, and I felt out of control. It just happened to stay under my weekly goal. I'm upset because I know I could've had a lot of delicious, healthy, filling food. I didn't need to stuff myself full of crap in a half hour window.

Then I would definitely refer to this as a binge. Just get back on the horse, it's all in the past now.

^^ This.
And, maybe look at incorporating small amounts of these foods during the week, and just relaxing a little at weekends, to get a better balance. It is not worth it, to end up feeling stuffed and miserable. Been there, done that too often to count. Have a few things you really crave at the weekend, but also balance it out with the healthy and filling foods.