Iron sights are any sights that aren't optical sights.
Open sights are any type of iron sight where the target is not encircled by the rear sight. Open sights are typically "post in notch" setup, but there are some other variations. The key is that the target is visible above the sights, not encircled by them.
Hooded front sights are sometimes encountered--usually the hood is there to protect the front sight, or to eliminate issues related to uneven lighting of the front sight. A hooded front sight is not considered to be an aperture sight.
The finer the notch and the smaller the post, the more precise open sights are and the harder/slower it is to acquire a sight picture.
Express sights, for dangerous game, usually have a very wide V notch so that finding the front sight is very quick and easy. Obviously in that case, carefully aligning the sights for a precision shot is very difficult, or maybe not possible at all.
There are some variants which have a wide notch with a much smaller notch in the bottom of the sight. These sights typically have a bead front sight--a round "bead" on a thinner post. This allows the shooter to rapidly acquire the sights for quick shots by placing the bead in the wide notch or to precisely align the sights by placing the bead in the small notch (sometimes referred to as "drawing a fine bead") when maximum accuracy is desired.
Another variant of open sights is the buckhorn sight. In this sight, the rear sight has projections that curve up around the notch like horns. This creates a sight picture where the front sight and the target are mostly enclosed by the rear sight. Typically buckhorn sights have a smaller notch in the bottom of the sight as described above.
Since, when dealing with open sights, the shooter needs to precisely align the front and rear sights, it is necessary that the rear sight be far enough from the shooter's eye to allow it to be in focus. An open sight mounted on the rear of a rifle receiver, for example, would be so close that precise sight alignment would be impossible. This is why rear open sights are mounted relatively far forward on a rifle.
Aperture sights are iron sights but are not open sights. The rear sight (and sometimes the front sight) encircle the target. The shooter looks through holes in the sights to see the target.
Peep sights usually have a relatively small rear aperture--sometimes the aperture is adjustable to allow for use in a wide range of lighting conditions. With a small aperture, the front sight and the target can both be in focus due to the pinhole effect. Also, the pinhole effect tends to minimize issues with the shooter's vision. However, a very small aperture requires very good lighting and can make it difficult to rapidly acquire the sights.
Performance in less than ideal lighting requires a larger aperture and by going to a larger aperture you lose precision and the pinhole effect is less helpful.
Note that the rear aperture is so close to the eye that it is blurred. The shooter shouldn't focus on the rear aperture, only on the target and the front sight. Because it's not necessary to focus on the rear aperture, the rear aperture can be placed very close to the shooter's eye allowing a longer sight radius. Sight radius is the distance between the rear sight and the front sight. A longer sight radius minimizes the effects of small misalignments in the sight picture.
The largest aperture sights are called ghost ring sights. They are so large and the ring is so thin that all the shooter can see is a "ghost" of the ring. They are usually very fast and can be used in poor lighting, but don't offer the precision of a smaller aperture. Also, because of the large aperture size, there is no benefit from the pinhole effect.
There is a sort of hybrid of open/aperture sights. This is when an aperture sight is mounted so far forward on a rifle (or on a pistol) that they are no longer blurred. In this case they act like an open sight. The front and rear sight now must be precisely aligned as in an open sight and the aperture is generally so large that there is no pinhole effect.
A little more information on iron sights.
Move the rear sight to the same direction you wish the point of impact to move on the target. Move the front sight in the opposite direction you wish the point of impact to move on the target. FORS (Front Opposite Rear Same)
Strong lighting from one side will tend to make the gun shoot away from the light. Unless the front sight is hooded/shaded, the light will make the lighted side of the sight appear larger to the shooter which tends to make the shooter misalign the sights slightly in the direction away from the light.