I just finished reading a series of posts on hit points. I'm not going to bother to link it, because there are many such posts and discussions and they are all more or less the same.
Hit points are a thorny issue and have been so since way back when. The barbs jabbing at the minds of so many involve the realization that characters with high hit points can survive seemingly impossible situations - a hail of arrows for example. After all, if a single arrow can kill a peasant, why does it take 10 to kill a fighter?
This question popped up often enough that Gygax wrote several essays about it, including the description in the DMG, p82. His explanation is always the same: Hit points represent fatigue, luck and physical toughness, all three, and a trick or two besides.
Folks have wrestled with this answer ever since. Some have tried to break it down into some kind of fatigue damage, vs. physical damage, etc. Others have argued that there are contradictions in this explanation, particularly as regards monster HP.
Despite the messiness, I never let it worry me much as a game mechanic, but the thread I just read wondered how Constitution should or should not affect Hit Points at each level, given the physical vs. fatigue aspect, and that seemed like a really legitimate question, given Gygax's definition.
The course out of this muddle begins with a simple realization:
Gygax was wrong.
Now, to those crying foul, I would point to a simple fact: Gygax had no more authority to talk about the meaning of Hit Points than Traci Hickman, Monte Cook, or Mike Mearls do. What I mean is that while he was certainly a very involved game designer - almost certainly the most involved in the '70s - in the D&D world, he didn't invent the concept of Hit Points. His explanation is his opinion. It is not the explanation of the designer.
Dave Arneson created the idea (and the label) of Hit Points. Dave Arneson didn't have a lot to say about what Hit Points meant. Luckily, if we look closely, its not too hard to figure out what he thought about them.
In the FFC he wrote "As the player progressed, he did not receive additional Hit Points, but rather he became harder to Hit"
For Dave, Hit points were a fixed number. It wasn't long (by 1972) before Dave changed the above so that while characters still received a fixed number of points, it grew greater at each level, but the principle in the second part of that statement "became harder to Hit" is really the most interesting. Dave's thinking was that going up in level equaled increased ability to survive. Ability to survive - the characters defense against death - is wrapped in three stats: Saving Throws, Armor Class, and Hit Points.
Armor Class has its limits. It's not much fun if characters and monsters are statistically invulnerable to being hit. The same limitations apply to saving throws. Hit Points are a lot more flexible.
For Dave, all three of these were subject to situational modification. Armor Class and Saving Throws could get a bonus of +1 to +4, and that's still common in D&D. Hit Point "values" (as he sometimes wrote it) were even more fluid; they changed from situation to situation. Arneson’s early gaming material often mentions "double (or more) values". the 1975 version of Temple of the Frog makes it clear that the key "defense value" of Hit Points could be doubled, trebled, even sextupled; ToTF: Pg 45. Breeding pond frogs “fight at Double value for 2-12 rounds” – but 3 hit points are the only value given; Pg 47. “double strength and HIT POINT VALUES”. (emphasis mine)
When Arneson created Hit Points for monsters and characters he didn't intend them to represent a one to one amount of physical damage a creature could take, or a one to one amount of luck or fatigue. They didn't represent anything concrete and interchangeable at all. Hit Points were a fluid abstraction for how many dice pips it took to turn it from living to dead or free to subdued. This amount could change from situation to situation based on the creatures willingness and ability to fight, mostly.
In short, 1 Hit Point does not equal 1 Hit Point. The value of a point is circumstantial and fluid and not the same from situation to situation or creature to creature.