It doesn't kill anyone to just answer it....
1) Usetime. The number of frames between when a weapon can be used. The Minishark has a Usetime of 8, so that means every 8 frames, it will fire a bullet. Terraria operates at 60 frames per second, so this means that it is ever so slightly slower than ten bullets per second (60 divided by 8 = 8.5, so you will get 8.5 bullets from it every second. Since you can't fire half a bullet, you can add another second on to that to get a whole number, so you'd have 17 bullets every 120 frames, or 17 bullets every two seconds.
2) UseAnimation: How fast an animation plays. Usually the same as usetime for melee weapons. A sword with a usetime/useanimation of 20 can be swung every 20 frames, or three times per second.
3) Shootspeed controls how many times a weapon fires during its useanimation. A Shotgun has a long useanimation (I don't know the specific number so lets call it 30 for the sake of explanation.) A usetime and useanimation will often be the same, to keep weapons like guns operating properly. So assume as Shotgun has both a usetime and shootspeed of 30. You can fire this gun twice per second. But Shootspeed controls the refire rate of a gun. So if you edited the shotgun's shootspeed to 15, the animation still plays for 30 frames. Sop you would actually end up with two shots from every use of the shotgun. a shootspeed of 10 would make it fire three times every time you clicked, while only playing the animation and sound once.
So if you gave it a shootspeed of 3, it would fire ten times per use, basically turning it into a fire hose at that point.
Editing these values independently of each other can make weapons do pretty stupid (and cool) things.