Not exactly.
The way it works (as far as I know) in UA, M&M, and Blue Rose is as follows...
If you get hit, you make a save vs. damage, using a Toughness score (or fortitude, in the case of the 'Injury' variant in Unearthed Arcana), against a DC which is based on either a semi-static (base DC of 10 or 15, or something like that, plus a modifier for the weapon being used), or else with (Damage Rolled / 5) + 15 (ala UA).
If you succeed, you manage to avoid being 'damaged' (i.e. a graze, or just a scratch).
If you fail, the result has to do with how much you fail. If by 9 or less (or something like that), you get -1 to successive saves against damage (i.e. you were wounded somewhat, and can't avoid injury as well). If you fail by 10 or more, you're rendered Disabled (like when you're at 0 hit points in a hit-point-based system).
There are all sorts of variations on the 'theme' of this sort of system, but that's the general gist. I haven't ever actually played a game with a Damage Save system, but I've gotten the impression that it's just a different sort of abstraction than HP.