IMO, sports is competitive and the study of budo is not; the former has rules and clear definitions of who loses and who wins - the latter has rules but there does not have to be a loser or winner; there is an exchange and both sides can be considered winners if they learn.
Now bar/street fighting is an entirely different animal, and contrary to what Dan says, there are really no rules - however, there will be conditioned behavioral responses based upon any martial training and other gender behavioral patterns that makes up the person - that is why men and women have different response actions in a fight - trust me, no one is thinking what to do next, they are simply responding based on their conditioned experiences and training. Of course, I think there are also some instinctive survival stuff going on as well, but that is so subjective it would be difficult to detail in a general discussion.
Now military combative situations are something entirely different and only those that have experience or training in that environment can provide any realistic information about that.
Operational definitions of fighting... A fight, to me, is something without rules, and there are survivors and maybe someone who shows mercy and doesn't finish the job.
a "scrap" or a "punch up" is more like what happens on the NHL or north american ice hockey, where there are unwritten rules about how long you keep going and you stop when the ref sticks his arm in.
A "match" is something with rules of engagement like MMA/Octagon/Judo/Karate/TKD cocmpetitions. They resemble fights, but there's someone there to stop it if it gets too real.
I've never been in a "punch up" or a "fight" but I've been in a lot of "matches" (judo) - only one of them ever felt like it was starting to be a "fight"... the ref intervened and calmed us down..
Combat - haven't done that, either, but hand to hand combat would be only after the air support, artillery, rifles, pistols, edged weapons were rendered inoperative or unsuccessfully deployed...