When holding down left click and moving the crosshair towards a viable target, the left hook will automatically fire as soon as the aim box appears on the target. With the right hook, it will only hook if the right mouse button is clicked when the box is already on a target.
This may have something to do with how Garry's Mod handles the difference between primary fire and secondary fire binds, as I glanced through the code and didn't see any major differences between how the left hook and the right hook identify viable points and grapple to them.