The training I've seen in "traditional arts for instance karate, kung fu, japaneses [sic] jujutsu and so-forth" has been less "real" than the ground fighting I've trained in CSW, BJJ, MMA, Catch wrestling, and Judo classes. In the Japanese arts, it's pretty much amounted to one-step sparring (including grappling) from seiza, a position I'm not going to find myself in too much outside of the dojo. In all "traditional" arts, the opponent never really resisted, and we couldn't put the techniques through a realistic feedback loop. At least with the so-called "sport" systems, you have to fight to get a hold, pin, or striking opportunity; if your mechanics aren't good, it won't work.
But to the original question, sport vs... let's call it "non sport" since I've seen guys get knocked out, choked unconscious, and have their limbs broken and dislocated in sport situations; seems like "real" damage to me. Sport fighting technique is obviously limited by the rule set, which varies from sport to sport. So you have no leg locks in Judo and have a set time limit to how long you can be on the ground, and no chokes or, I think, a closed guard in Sambo, and no leg locks or neck cranks at various levels of BJJ, or no headbutts or certain strikes in modern MMA. Non sport rules aren't limited by technique. The biggest difference-maker, though, is objective. In sports, under most ground fighting contexts, you WANT to engage on the ground (though not always; note the abilities of MMA fighters like Chuck Liddell and Mirko Filipovic to stay or get back to their feet) where in the non-sport context, you're usually trying to disengage and escape (though again, not always; I've had to hold people down in decidedly non-sport situations so they wouldn't hurt themselves or others). The change in objectives and the openness of the arsenal means that the two will rarely look alike. However, someone who is skilled in sport ground fighting will have an advantage over someone who isn't. I know what it's like, for instance, to try to get to a safety position while defending strikes thanks to my "sport" MMA training. A friend of mine actually used ground-and-pound defense that he'd trained just a few weeks prior to getting jumped; if it hadn't been for that training, he would probably have been the victim of a beat-down. I also know what it's like to sweep or reverse a bigger, stronger guy who's trying to hold you down thanks to my "sport" submission wrestling and BJJ training. If it works against a resisting opponent, it works, period, no matter what the venue is. You just get to spice things up as new variables are introduced. The same motion I've been using for years to set up an arm bar from guard suddenly creates the correct angle for me to knee and hammer fist the guy in the head until I can escape, reverse, or submit (snap). Without the ingrained hip movement, it wouldn't be possible.