Telescope maker and optician here.
You're talking about two separate things, different yet related.
Telescopes
When it comes to telescopes, the "artifacts" are called diffraction spikes. Most telescopes are complex optical systems that reflect light on a succession of different mirrors. Usually there's a secondary mirror suspended at the top of the instrument. The device holding the secondary mirror is usually called a "spider", and most of the times it's connected to the main optical assembly (the tube) via 3 or 4 elements called "vanes".
https://i.imgur.com/rSGLJBc.jpg
https://i.imgur.com/159HDJv.gif
Incoming light, hitting a vane, is diffracted - at the edge of the vane the light is scattered in a direction perpendicular to the vane, producing a diffraction spike. In fact, each vane makes two spikes, opposite to each other. For reasons too complex to explain here (that would be a medium-to-advanced class in applied optics), the spikes appear centered on the image of the star, not in the middle of the vane.
3-vane spiders make 6 diffraction spikes. You've seen the pattern. 4-vane spiders make 8 diffraction spikes, but they coincide 2 by 2, so they look like only 4 spikes. You've seen that pattern too. 8 separate diffraction spikes are also sometimes seen (more rarely). In fact, any even number of diffraction spikes can be produced by a system that uses straight vanes for the secondary spider.
This is the explanation for the star images you've seen captured by modern telescopes.
The human eye
The eye obviously does not have spider vanes. However, as an optical system, the human eye is plagued by numerous defects, called aberrations. Its lenses are by no means perfect - far from it, in fact. The image, as projected onto the retina, is actually of rather poor quality. However, since the eyes are moving constantly, your brain interpolates successive images and is able to restore some clarity from multiple successive images seen at slightly different angles.
Yet even so the system is not perfect. Tears flowing on the cornea distort the image slightly. Dust motes produce diffraction - of an irregular shape. The pupil is not like a smooth round opening, but its circumference is jagged - more diffraction there. The optical media in the eye are not homogeneous, and so they further change the image. The eyelashes cause even more diffraction.
Most of the time this doesn't matter much. The images are low enough contrast that these defects are not seen. But there are some very high contrast images where all defects become clearly visible - the bright stars on the dark night sky. Every imperfection in the eye is revealed by this challenging performance test.
Go outside at night and look at the sky. What do you see? Are the stars perfect little round dots? No. They looked jagged, spiky, irregular. Their shape even changes in time. The brighter the star, and the darker the sky, the more jagged the image. It should be noted that the star images seen with the naked eye are irregular - however, for simplicity, when drawn on paper they are shown in simpler forms, hence the star of David, or the regular patterns of radii surrounding a central dot, seen in some old drawings.
This is true of human vision at any moment in history. The way we see the stars now with the naked eye, the same way they were seen long ago. People looked at the sky and made drawings of what they've seen. The drawn images are not perfect, sometimes there's a bit of interpretation, but as a rule they show how imperfections in the human vision alter the way we perceive the world.
To sum it up, both telescopes and human eyes modify the images they receive. The patterns look somewhat similar (yet not the same) because the phenomena are similar (yet not the same). It's not surprising at all, really, that the ancients represented the stars in ways that resemble, somewhat, patterns seen nowadays in modern telescopes.
