Two different functions. I use the AF-On button only to focus. The shutter button does not focus. Focus is different from the shutter release.
Setting a1 is the shutter release. It tells the camera whether to take a photo even if focus is not locked on (release), or requires focus to be acquired first (focus). It does not matter whether focus is by AF-On or the shutter button (or manually for that matter). This setting asks whether focus is locked in, or whether it doesn't matter, before firing the shutter when the shutter button is pushed.
Think about it this way, if you have a1 set to focus then the shutter will not fire until focus is locked and the green dot comes on in the viewfinder. With a1 set to release you will take a shot whenever you hit the shutter button regardless of focus.
Try using both focus and release a1 settings to take an out of focus shot. If your shot is out of focus, and a1 is set to focus, the shutter will not fire. The beauty of digital is that you can try all of the different settings and see the results without the hassle of film.