They are not doing so. You are imposing that on others.
You've had answers. Recovering hit points is recovering drive and the will to live. Recovering hit points is having heart lifted and tiredness ebb away. Etc. You then ask about how hp differ from exhaustion levels, without (i) explaining how that works for you in 5e (where you have tiredness causing penalties to action, but injury doesn't, and tiredness being harder to recover than injury is - I find both those things quite absurd based on my own experiences of exhaustion and of injury) nor (ii) explaining how either injury or exhaustion differs from stat loss (say, a shadow's STR drain in 5e, or poison in 3E) and how the PCs know that healing magic won't alleviate this but will alleviate that nor (iii) explaining what HD are in 5e.
You are able to cope with the seeming incoherence or dissonance that your conception of hit points generates in relation to (i), (ii) and (iii). Presumably others are able to cope with what you take to be incoherence or dissonance in their preferred narrations of hp loss and hp recovery.