Olympic shooting is about accuracy, not a round's effect on the target, that is why they now use .22 caliber or air powered. .22s and air guns are less regulated worldwide, so more countries can compete. They used to use larger caliber firearms but have gone the way they have because it makes things more competitive.

"Sport" shooting is recreational shooting. So going out to a range and putting holes in paper for fun is sport shooting. Sport shooting is also competitive non-olympic shooting competitions like 2 or 3 gun, where you are competing for time to hit a number of targets while moving using a pistol, rifle, and shotgun.

As far as hunting with a semi-auto goes, it isn't really all that advantageous unless you are doing pest control for large numbers of animals, like a team of hogs. You can't usually shoot more than one game animal in a short period of time, so faster successive shots isnt needed.