I treat HP, for the most part, as minor scrapes, nicks, or blows to the character's body. It is essentially more 'plot armor' than it is actual dangerous damage to the body. The exception is when the HP runs out and you are actively dying (below zero HP). Then you have taken a deadly wound that will end up killing you if not addressed.
In your example of a Rogue getting hit with a bullet, I'd likely describe it as a hard impact to their body that is going to develop a gnarly bruise if not healed with magic. Their armor might be dented or frayed from the impact and their ribs/appendage sore but functional.
Its only when things like bleed or poison come into play that we really have to deal with punctures to the body that aren't life threatening. Bloodloss itself from bleed is actual bleeding but chips away at the 'plot armor' continuously and poison, well, you don't need serious damage for poison to get into your system.
I just tell the player that their character took damage, i.e. "You are attacked by the bugbear. he strikes you and deals 8 points of damage". And leave it at that. Hit points are an abstract mechanism that does not directly translate to physical damage, it also covers bruising, general fatigue, ad anything else that moves you closer to incapacitation. Describing the ACTUAL damage to the body is not needed, and could leave to play complications. i.e. "You said I injured his hand, how is he able to hold a knife?"
Hit points are an abstraction used to make playing easier.
One way to think of it, as mentioned, is minor nicks and bruises from the character almost avoiding being seriously wounded; up until the last blow that takes the character to 0 or less hp. The minor damage slows the character down until they can no longer avoid being hit squarely.
Yeah, I treat hp above the first hit die as narrowly avoiding serious injury. So it might be a cut or scrape, a bump, or just intense exertion to avoid that serious injury.
Only in that last hit die worth of HP do you experience serious wounds.
At least that's how I imagine it.
From a practical standpoint, we don't describe what the damage represents on each hit, except on particularly large amounts of damage.
John Wick.
Both to myself and to my players when DMing, I think of hitpoints not unlike what the character John Wick goes through in a movie. No single blow is fatal. There's just this relentless accumulation of exhaustion and wounds that will - if not addressed properly - result in death. Mostly I refer to injuries that involve blood.
In-game non-lethal is more like the punches and little falls he takes. They won't kill him but they'll eventually incapacitate him.
The two interact nicely.