Whenever a replay is shown with footage from the high speed camera, slow-motion footage is shown. Why do they show footage from the slow speed camera and call it the high speed camera?

The team "high speed camera" refers to how fast the film is going through the camera. To get "slow motion" you film far more frames per second than usual, then replay the film at a normal frame per second count. Typical TV playback is 24 frames per second, so to show something 3x slower, you have to film 72 frames in one second, or film it 3x as fast.

http://en.wikipedia.org/wiki/High_speed_camera

Please, try to google questions like these in the future.

You can see the bullet in slow mo but not normally so they use a high speed camera to capture the flight and replay it in slowmo to get the information they need.

Video is normally shot at 30 frames per second. A high speed camera can record frames at much higher rates-up into the 100's. These frames can then be slowed down to the normal rate of 30 fps and the motion will appear much slower and allow you to observe motions that happen too fast to normally see. I'm not sure what kind of camera they are using because they don't show it up close enough to read the label, but the appear to be recording direct to digital on a laptop and then playing back digital slow motion.
Death-you're right about the principle but wrong about the fps. Standard for sound film is 24 fps-NTSC video has always been 30 fps.

the high speed camera is only as fast as the projected amount of user info

hi my name is adam statham from england uk and i saw a system in the birmingham nec motorcycle show called the flash back system i was basicly what looked like two flash gun bulbs and a sensor in the middle and the salesmen took my number plate and took a photo of it the moment the flash went off on the camera the system started flashing at a very high and bright speed and all the camera got was a blank very bright flash back on the camera so my friend and fellow biker bought one and he installed it on his bike he went through a speed camera without realising he was speeding "honest officer" and he got flashed but he did not get a ticket but a week later a traffic cop pulled him and noticed the thing above the number plate he was a biker himself he took a photo and the same again my mate got done for trying to pervert the course of justice and 6 points on licence and £2000 fine ouch all that because of £75 so i have seen this work with my eyes and my mate paid the price but i have never seen the system again.