If you push the button half the way to lock the focus, move the camera to get the composition you want, does that change the exposure or is it locked in place like the focus?
On a 300D here's the Short Version (I'm sure other Canons are about the same):
Pressing the shutter halfway down locks the focus. It also takes an exposure reading at the same time. Recomposing will keep the same focus if you hold the shutter down, but the exposure reading will change as you recompose.
Pressing the AE Lock button when you press the shutter down locks the exposure. Now you can keep the same original focus and exposure during recomposing OR you hold the AE lock button down and take a series of pictures. The original exposure is kept as long as you hold that button down but you can change the focus point between shots.