The Eye, and Camera Lenses
I think I understand what your issue is here.

Often, in diagrams of lens systems and eyes, the diagram will only show rays parallel to the optical axis (see here). Although many optical systems are designed so they are optimal for this axis, off axis rays respond in a fairly predictable way too. This figure shows an off-axis point source, which focuses at a corresponding off-axis point on the other side of the lens.

So, there is "one focal point", as you say, for each position of the object relative to the optical axis. In optics we generally talk about a focal plane rather than a point, as the focal point only refers to cases of idealized point sources, lasers etc.

Now, the aperture (pupil) is a completely different matter. This provides a limit to how well an optical system can focus. When the aperture is small, it can focus really well, but not much light can get in. When it is large, the ability to focus is reduced but it allows one to see better in the dark (increasing the signal to noise ratio). Focusing requires all the rays from a source to end up at the same point on the retina/film, the aperture, when it is as small as possible "selects" only those rays that will end up focusing at exactly the right place (assuming the lens focuses to the right place, which it does not in the case of the short or long sighted). This selection cuts out a lot of the light, and often it is good to trade off the ability to focus for the amount of light. Without going into detail, this large aperture results in the focal ability of the optical being strongly dependent on how far away the object is (see this).

Your question is rather open ended, but I hope this is what you were getting at.