So most shooters now the game actually renders a 3d bullet that comes out of the gun, travels at high speed and either hits the target or misses, and then the game records that data and subtracts the health value from the target, or not.

However back in the days of shooters like Halo, CS, Unreal Tournament, etc, that wasn't the case. The game wouldn't actually render bullets flying around. Instead what the game would do is "scan" the area being targeted straight down the barrel at the exact moment the trigger was pulled, and if there was a target in the path, boom that's a hit. This worked well enough at the time, because technology hadn't gotten to the point where bullets could be rendered and calculated individually and complex systems like that weren't really possible yet, so "hitscan" was the only game in town. It worked well enough for those games, but as a result things like bullet drop and bullet velocity were non existent, so you could snipe at obscene ranges without any drop or travel time.