Most people have the same eye and hand dominance. I was surprised to find that I am left eye dominant last year when my eye doctor was thinking of prescribing me contact lenses that correct distance vision in one eye and near vision in the other. It explains why I putted and swung left handed even though I am right handed. It could also be the reason of my poor sight alignment in my shooting class in high school because I was not using the right eye to aim. I mean the “left” eye which should be the right eye.
I just came across an article regarding cross-dominance. It stated that someone is cross dominant if he is having a dominant eye on the opposite side of his dominant hand, as in my case - I am right handed but left eye dominant, which could make using the of a rifle or shotgun a real challenge. So for someone like me, who's right handed but left eye dorminant, if I shoot with my right eye, my shots will stray to the right. I would have to shoot with the rifle from my left shoulder instead of my right shoulder to get a more accurate shooting. Not that I am interested in hunting, I am just illustrating the impact of cross dominance. By the way, I don't own any firearm and I am strongly against people owning one. It creates more gun violence and accidental deaths.