When we say “pain” do we mean the firing of the nerves, or do we mean awareness of it?

I'd say awareness of it, especially considering AFAIK local anesthesia (as in, fully awake during) doesn't stop the nerves from firing, just from the signals getting to the brain, and I'd say that's blocking the pain.^

Also there's an interesting point in there: (this is not a rebuttal, just an addition)

Doctors used to assert that babies didn’t feel pain, because 1) they couldn’t tell us about it, and 2) they didn’t remember it later.

The reason doctors nowadays use anesthesia, (besides it being squick-y not to) is because it was discovered that, (though they may not consciously remember it) it can manifest in PTSD and other trauma related disorders later in life.^

In addition, it was found that there is a heightened level of stress hormones during surgery on infants, which were absent in surgery done with anesthesia.^ (These stress hormones also increased the risk in post-operational complications, due to the hormones acting to break down carbohydrates and other fats in the infant's bodies)

Note that you're getting into something that was a big deal in the 70s and 80s. They'd perform any surgery on babies without anesthetic (which is dangerous to babies) because it was believed that they wouldn't remember anyway so it wasn't a big deal after all. I suspect that people will learn about this with horror.

To be fair, dosing babies with anesthesia is way more difficult, and there’s zero record of whether they have any drug allergies or intolerances

To the best of my understanding this is why local and general anesthesia can be the best combo.

General keeps you from being conscious of the damage of the knives during the surgical procedure. Local numbs the area to keep the brain from being aware that damage is happening. Reducing trauma sounds like a good idea to me.

Pain is fascinating (particularly if you're not the one experiencing it.) Two people experiencing the exact same nerve stimulation can be painful to one but not the other. Context, life history and experience, and expectations all play into the experience of pain. In general, your brain determines if something is painful, then you do or don't experience that pain. People can be shot or stabbed and be completely unaware until the brain decides it's time to let them know.

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