I think the parent poster if confusing general anesthesia from sedation [1]. If you got a colonoscopy or your wisdom teeth out, it was probably sedation. If you got major surgery where they cut a big hole in you, that's more likely to be general anesthesia.
"Twilight sedation" is pretty spooky from a philosophical perspective. You are somewhat aware of what's happening to you and are experiencing it in the moment. But you are unable to form long term memories of it, so after the procedure, it's like it didn't happen. But there was a point in time where they you that you were was at least somewhat conscious of the procedure.
Quite possibly, I don't know the difference - as a kid I had to have serious orthodontic changes to my teeth as none of my baby teeth fell out and grew to the size of adult teeth.
One of the last surgeries I had, which was breaking off 4 molars, I felt like I was going to explode breathing the gas - like really painful pins and needles everywhere, my eyes actually opened and I felt like they were rolling back into my head (think pain of a really bad migraine but in your eyes).
Fortunately they closed my eyes, and it stopped but I couldn't speak, next thing I know my mouth is being held open with a vice, very painful, but I couldn't see, couldn't talk (wouldn't have been able to anyway with the jaw vice).
Aside from remembering panicking further, and occasional fuzzy memory of pain followed by (I guess) being unconscious again, that's all I remember of being awake.
When they finished I had to be slapped hard across the face at the end multiple times (this was the 80s), probably because the anaesthesiologist had O/D'd me on realising I was still awake. I was later told they were considering taking me to hospital because I wasn't waking up - this was the last time I had dental surgery.
About 5-6 years later they banned the gas they used on me in the UK.
I may need some routine (real, hospital) surgery in a year or so, and now I can't stop thinking about last time I had the above, I even started googling chances of being awake etc etc (because it does happen) and really wish I hadn't.
The other aspect of twilight sedations is: do you feel pain and then lose the conscious memory, but retain the stress reaction's affect on your body?
And similarly for anesthesia: even if you don't feel pain, is your body having a stress reaction? Obviously yes to some extent, for the non-neural pathways that are physically insulted during the procedure, but what about for neural pathways?
I've helped a couple of family members who have gone under the sedation that you're talking about. I don't care how much more dangerous or more expensive general anesthesia is. I'm taking that option every time. I never ever want to be under the sedation you're talking about.
That sedation takes hours and hours to wear off, where you're worse than helpless. Completely memory free for hours after the surgery is over and can barely function. It's terrifying.
Meanwhile, when I've woken up from general anesthesia the few times I've been under, I'm almost immediately perfectly conscious and able to function on my own and remember things.
When I had my wisdom teeth out, I had a "dream" that I was on a old wooden mine-cart styled roller coaster with wheels that were sparking dramatically against the rails first on the left side, then on the right. (mirroring the teeth removal)
"Twilight sedation" is pretty spooky from a philosophical perspective. You are somewhat aware of what's happening to you and are experiencing it in the moment. But you are unable to form long term memories of it, so after the procedure, it's like it didn't happen. But there was a point in time where they you that you were was at least somewhat conscious of the procedure.
[1]: https://en.wikipedia.org/wiki/Sedation