Martial sport (ספורט לחימה) is a form of competition that uses only a specific set of fighting techniques to compete in a set time-frame and arena.
Martial sports such as MMA, differs from Martial art and self defense systems not only by the variety and type of techniques, but in it's the main rational - The main goal of martial sport is winning a competition. The goals of martial arts can include winning, but tend to have a longer time-frame.
Martial sport usually develops high ability in a predetermined set of combat techniques and thus might help to achieve other goals in actual non-competitive fighting.
A list of martial sports documented on AKBAN wiki
Video of Judo competition
Video of Taekwondo competition