I like the way we do it in Hero System. You have two relevant stats: BODY and STUN.
BODY represents serious damage. You might have a high BODY because you're a 9-foot-tall behemoth, or you're a regular-sized person whose got an incredibly strong will-to-live, or what-have-you. That stuff is flavor; the important thing is, high BODY equals hard-to-kill. A typical human has 10 BODY. When you reach 0 BODY you are Dying. You can go to negative BODY, which is very bad; you lose 1 more BODY every Turn if you are at 0 BODY or less. Your character dies when they reach negative their normal maximum positive BODY.
STUN represents ephemeral concussive damage. You take STUN damage from a lot of minor things, non-lethal electrical devices, a cold or flu, whatever. A typical human has 20 STUN. When you reach 0 STUN you are Unconscious. You can go to negative STUN, where you are basically deeply unconscious, perhaps even comatose.
You have a REC stat (short for "Recovery") which represents how fast you recover from physical stress and trauma. A typical human has 4 REC.
BODY damage recovers very slowly. If you are resting full-time in an environment conducive to recovery, you get back your REC in BODY points every week of rest. An absolutely typical human who was Dying at, say -2 BODY when they reached the hospital, will be fully recovered on BODY after three full weeks of bed rest.
STUN recovers very quickly. You get back your REC in STUN points after every Turn in a fight (a Turn is 12 seconds long, and the typical human will get 2 actions in that time), and you can get it back sooner if you spend actions to "catch your breath" or "shake it off." An absolutely typical human who was unconscious at -4 STUN, will be fully recovered on STUN after 6 Turns, or a little over a minute.
It's not super-realistic, but then, neither is hit points. It does feel very cinematic, though, and lets players feel like the characters in an action movie, which is something I like.