You've just discovered the difference between line-of-sight [LOS] (and its partner line-of-bore [LOB]) and trajectory [TRAJ]. The difference you are seeing is amplified by the slugs you're shooting -- big and slow as compared to a rifle bullet that is lighter and faster.
We'll walk through a bore sight procedure for a scoped rifle using a laser bore sight that will serve to illustrate our points.
1. Imagine a centerline that goes vertically through the center of your barrel and the center of the scope -- this is the elevation centerline. These centerlines should be in identical planes (on top of each other).
2. Imagine a centerline that goes horizontally through the center of your barrel and center of the scope -- this is the windage centerline. These centerlines should be in parallel planes or parallel to each other.
3. The first thing to do is to do is to get the vertical centerlines of the bore and scope to match. Imagine a crosshair in the center of your bull's eye at 25 yards. With your rifle in a rifle vise, you insert the laser bore sight in the barrel bore and adjust the laser dot on the target bull's eye crosshair center. Now adjust the scope windage adjustment right or left until the vertical crosshair is in-line with the vertical cross hair on the target.
4. Use a torpedo level to check the rifle's receiver for level; then do the same thing by putting the level on the scope's elevation knob. When both are level, it means that the horizontal plane of both the barrel and scope are the same; that is, both are parallel to each other. Adjust the elevation knob of the scope to put the horizontal crosshair about 2 to 3 inches above the centered laser dot on the target. You now have a rough 100 yard zero on the rifle. Both of these actions are done by making the LOS for the scope and LOB the same in the vertical and parallel to each other in the horizontal plane.
5. However, a bullet or shotgun slug does not fly to the target straight and true like the laser beam. The bullet or shotgun slug follows an arc called a trajectory. Think of it like lobbing a stone at some point in a pond from the shore. You see where you want to hit with your eye (LOS) but you have to lob the stone to hit the point; that's trajectory (TRAJ). When you set the horizontal crosshair about 2 to 3 inches above the laser dot on the target at 25 yards. You were compensating for the trajectory of the bullet to get it to hit the center of the target bull's eye at 100 yards.
6. With the laser bore sight, what you've done is establish a "coarse zero" for your sight at 100 yards. Now you go to 100 yards and actually shoot at the center of the target with live ammo. Assuming you have the correct position and don't disturb the rifle while firing, you'll fire three shots for a group. Plot the center of the group and move the group up or down, right or left to shift the center of the group to the center of the target using the elevation and windage knobs of the scope. Fire another three round group. Adjust and repeat as required until you are sure that you hit the center of the bull at 100 yards when the scope crosshairs are centered on the target. You have now established the "fine zero" for the rifle.
7. A shotgun slug is not as accurate as a rifle bullet and its trajectory has a much greater arc than that of a rifle. The shotgun slug is not as aerodynamic as the bullet either and this also affects the size of the group on the target (the technical term is called "dispersion"). The idea with a slug gun is to keep the slugs in as small a group as possible (this is a function of your barrel, the brand of slugs, and kind of slug you are shooting) at the approximate range you plan to engage your target. Most slug gun shooters will zero theirs for about 50 yards.
8. Some slug guns are quite accurate at 100 yards and you can zero for that range if you have a barrel and slugs that can do it. You will only find this out by experimentation with different brands of slugs and the various ranges -- 25, 50, and 100 yards. I have found that if your slug gun can shoot a small group about 2 to 3 inches above target center at 25 yards, go right to the 100 yard target and see if you can get it to group. If you can, don't worry about the 50 yard target -- if you can hit the 100 yard target with a good group -- just adjust the sights to fine tune them to hit at 100 yards. You will certainly do well at 50 yards. However, if you cannot get a group at 100, drop back to fifty and try to get a good group there. You'll have to adjust the sights for grouping at 50 yards. If you get a good group there, then that is what your effective zero is with this barrel and brand of slug. Don't bother with 100 yards shots, because you can't be certain of a good hit with this combination of barrel and slug.
Those 12 ga. slugs make some pretty big holes! Don't get the magnum slugs, though. The standard 2-3/4 inch slug has nasty enough recoil when sighting-in from a bench. If you use the magnums, all you'll do is drive up your cost of ammo and develop one heck of a flinch from the additional recoil. Remember that slugs, when fired from a bench, will amplify the felt recoil. If you get to the point that your shoulder really hurts or you're anticipating the punch from the recoil or you start flinching -- unconsciously trying to get away from the recoil -- or you are jerking the trigger, it is time to go home and come back another day. Zeroing a slug gun can either be a piece of cake or a nightmare from Hell. If it's the latter, don't fight it. Just go home and come back when you're fresh another day.
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