The real issue here is what does damage mean. This is one of these situations that exposes the absurdities relating to hit points.
A fireball is supposed to be set alight unattended objects but anything that hot is likely to kill a human. If only by damage to exposed mucous membranes and eyeballs and such.
There was a discussion* not very long ago** about the nature of damage and hit points. Folks seem to be divided*** into three**** groups on the matter.
The first group insists that hit points represent the amount of
physical damage a body or object can take before falling unconscious or breaking apart. That fireball burns you a lot, or it burns you only a little, or it barely burns you at all, but the point is that
fireballs burn you. They don't scare you or exhaust you or bum you out, because that's not how fire works. So now everyone in the world has super healing powers and can bounce back from nearly being burned to death in just 8 hours, and a fighter can just decide to not be burned anymore as a Bonus action. Uh huh. Sure, whatever keeps the game moving.
The second group insists that hit points are more
abstract, that they represent an aggregation of physical, psychological, and physiological effects that can vary depending on the situation, and requires you to play fast and loose with what "reality" looks like. Did you take full damage? It probably burned you. Did you take only a little damage? Probably just stressed you out. Unless the cleric healed you with magic, which means you were actually were burned after all.
Unless the cleric ran out of spells and needed to rest to get those spells back: when you wake up it turns out those burns are gone, so they must have just been exhaustion.
UNLESS you slept in your armor; you wake up exhausted at full HP so it must have been, I dunno, depression or something? Schr
ödinger's Burns: they're both present and absent and you never know which until you heal them.
The third group mostly just shakes their heads, crosses off one number and writes down a new number, and
tries not to think about it. Damage and hit points and ability scores and stuff are all just numbers that move around behind the scenes anyway, and all of them are nonsense from a narrative perspective. The City Guards don't brag about who has the highest Strength score, and wanted posters don't have Challenge Ratings of the various villains printed on them, after all. So they try to stay immersed in the story and not let annoying little things like math district them. Did that fireball burn you or not? Who cares, just cross off 22 points from a box and move on.
I'm usually in the third camp as a player, and the first camp when I'm a DM (I'm fickle). But really, all three are perfectly acceptable if you want my honest opinion. Is fire a chemical reaction or a philosophical quandary? Both hurt my head.
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*argument
**every three months
***willing to die on this hill
****at least