In the 1e DMs Guide, Gygax describes what he means by hit points. Heh. He is the source of all of the later conflicts about how to interpret hit points.
Essentially, there is a doublestandard.
• For player characters, hit points are almost entirely nonphysical.
• But for monsters, hit points are almost entirely physical.
This doublethink allows players to ignore the inconveniences of actual wounds. At the same time, the DM can go into gory detail about hacking up a monster for its visceral entertainment value.
Unsurprisingly, there are some further inconsistencies. Despite describing the player character damage as nonphysical, the amount of time it takes to heal might imply the healing of actual wounds. When Gygax describes the Constitution bonus to hit points, his example (Rasputin) goes into graphic violence to describe the ability to survive many death-dealing physical injuries. His main point seems to be, some individuals have high Constitution, while others dont. But by extension, at least the hit points that come from Constitution seem to refer to physical trauma. That said, Constitution is also responsibility for avoiding fatigue, so that implies buffing the nonphysical hit points too.
Anyway, we happen to know what Gygax thinks about hit points, and it is complex and inconsistent, depending on which context one is describing when referring to hit points.
In my view, 4e and 5e have the best systematization of the conflictive D&D traditions about hit points.
From max hit points until half hit points is strictly nonphysical, except for allowing some glancing contact if dealing poison or similar contact effect.
At half hit points, the creature becomes "bloodied". The damage is still mostly nonphysical, but there is cosmetic superficial physical damage, the kind that leaves bruises and requires bandages.
Only at zero hit points, can there actually be a deadly wound − the proverbial sword thru the gut.