Yes, pain is pain. People can still feel it and suffer even if they do not remember it. Anesthesia in context of surgery is too complex of a topic for me to comment on but I do frequently manage patients that are sedated, on ventilators either going to or coming from surgery. There are different scales and tools we use to assess if someone is under sedated or in pain. Keeping explanations simple pain can reflect as changes in vital signs, rigid or tense muscles, facial expressions. Sedation in the context I’m referring to is more a scale of either how awake someone is or what type of stimulation they respond to, for example do they open their eyes if someone says their name? Or do they open their eyes if I gently tap on their shoulder or do I need to put pressure on their nail bed for them to respond, if they respond at all. If they’re sedated enough they won’t remember the pain but they would still feel pain. Again this is NOT referring to general anesthesia during surgery, that is too complex and anesthesiologist have a very difficult job ensuring people are adequately medicated for surgery while also ensuring that they treat the side effects of the anesthesia medications so they don’t just kill people.

The two do have some overlap and my previous statement assumes no chemical paralysis. There are also times where it is acceptable to just sedate someone, or do something emergent without sedation and then giving something like Versed which causes retrograde amnesia. The person may have been fully conscious and felt everything that just happened but still won’t remember it.

This is a bit of an oversimplification but I’d say firing of the nerves is pain. I don’t have literature available to support but I know giving babies anesthesia is very dangerous so I would like to believe that the reasons you listed where just an over simplified “it’s really okay to do X or Y because they won’t remember it” rather than explaining to a parent in a way that they would truly understand the risk of anesthesia for a baby AND still allow whatever procedure to be done or force a parent to knowingly elect to put their baby through pain and suffering for a procedure. But again, not a doctor and I don’t work with people/babies during surgery