As noted above , the recommended sight picture for a target is to focus on the front sight & the target & the rear sight will be out of focus but it works.
Now that is for a target that is stationary. Does the same concept work on a moving target such as a clay bird ? I am thinking of taking up trap & would like to know. I am thinking that the front sight on the shotgun barrel would be the place to focus ?? Thanks.
The two are essentially opposites of each other.
With pistols, the idea is to focus on the front sight with the center of the target in the background (center of mass, as it were). The rear sight and the front sight are, for all intents and purposes, at the same depth of field so you can see them both (at arms length, objects 4 - 6 inches apart will both be in reasonable focus).
What others have said about shotguns is true - you "point" the gun, keeping your eyes on the target at all times. NEVER change your focus to the bead or the barrel. And especially, don't be lining up a mid-bead and front bead as if aiming (this is okay when mounting the gun before calling for the bird, but doing this creates bad habits for when you're in the field and you have to mount the gun instinctively).
What has not been mentioned yet, is that shotguns designed specifically for trap and other clays sports are designed differently than shotguns designed for hunting. When using clays models, the bird should be mostly visible above the rib (or barrel, if no rib). Conversely, field models require the target to be covered when the sight picture is optimal.
If you use both types at the range or in the field, you can be over or under the bird depending on which sight picture you're using with which gun. 99% of shooters can't easily adjust their sight picture from one situation to the other.
To combat this, what I do is use only trap models at the range and only field models in the field. This way my habits in both places become ingrained and are consistent with the model in use.