The bullet is harder to dodge. Because it's faster.
You can dodge fewer bullets than axes before you die.
HP isn't meat points. HP is "Avioding death" points. Bullets are so fast you lose options to avoid death by them.
HP is an abstraction. HP ≠ Injurious capacity. Relative Dmg ≠ Relative lethality if you are struck with the weapon.
If I am cut in half with a katana, I die. If I get hit by a gun's bullet through any of various major organs, I die.
Guns have a lot of ways of killing me, and are much harder to dodge. I can dodge them a certain number of times reflected by my class and my Constitution, but eventually, I tire out and can't dodge bullets or get lucky enough that they aimed poorly, and I get nicked in the arm. I'm bloodied.
If I keep fighting without some rest and healing, I'll likely get hit in a more lethal location quite quickly. This is reflected by the amount of HP damage I'm taking from the gunfire.
I understand the OP's confusion though - D&D uses the term Hit and Damage in jargony ways, and CRPGs have primed us to think that hit rate = whether I impact or not, and damage dealt = once I impact with weapon, how much that afflicts the target.
Really, HP is like a fifth wall of defense. You've got your AC and your three saves to protect you by reducing or entirely mitigating the effects of an attack. But once you've done that, your HP is your bucket of luck, fortitude, reflexes, and willpower to survive what otherwise would be the end of you. I used those terms quite purposefully: in 5e, those are saves you roll, but you should also consider how they play into your HP. Fortitude of course is the most aligned with HP as it's reflected by your Con score. But think also of HP as your ability to dodge, your ability to push through the pain, your ability to stand firm against pushes and bludgeons. It's your ability to say to the God of Death, "not today."