It actually changes from game to game and setting to setting.
For example, in nWoD Mage, spirits do not as such have hit-points, they have Essence. Once they run out of Essence, they cannot hold themselves together anymore, they begin to loose their form and the very core of their existance, their 'soul', is in danger of evaporation. You could say that damage to their Essence is loosening their confidence and faith in their own abilities and core behaviour. It is possible to directly leech off essence from spirits, but you can also damage them by shaking their confidence to what they are and what they want to do.
Mortal creatures still have hit-points though, albeit there is differentation between bashing ("shock/blunt") damage, lethal damage (bullets, normal supernatural attacks etc.) and aggravated damage. Loose your hit-points to blunt, you lose consciousness and any further blunt damage upgrades the bashing damage to lethal damage. Lose all hit-points to lethal damage, you die in short order, though you are in pain long before that. Aggravated damage is just nasty, it's akin to lethal, but very hard/impossible to heal fast and allows for a myriad of rules and effects to be applied to you (such as magically sapping your Willpower or mental stamina to empower others). Think of aggravated damage as badly broken bones, mangled intestines, doused in holy water for vampires etc style Big-Nasty-Need-Hospital-Now damage.
In Cyberpunk 2020 you got stat and skill debuffs based on the damage you carried around: you lose half your hit-points and you were making stat check to stay conscious, to crawl around and your effective stats were something like halved.
Then there are the Redshirt points in the RPG Starwreck. Any damage to your squad while on away mission killed redshirts. Once all redshirts were gone, you had to make stat throws against all succesfull attacks; fail and you died, period. This is very much akin to your 'luck' system.