It doesn’t matter because a response is not there in a form of a heart rate, adrenaline, etc. There’s no sign of the whole chain of imminent reactions that pain creates. And when an anesthesiologist sees it, they stop the procedure and act immediately. If there’s no psychological trauma after you wake up, you felt nothing. But it may be if a team was negligent.

i'm not convinced that either one is equal to death

I can’t see why. Imagine you’re unconscious: anesthesia, fainting, dream, coma, knockout. Is there something else that must happens to your consciousness that will make you dead? To me it’s like turning off the main switch when lights are already out. You just can’t Alexa turn them back on, that’s it.