In the case of dithering, that’s only because the monitor has insufficient resolution. Put a 1:1 Floyd steinberg dithered image on your phone, hold it at arm’s length, and unless you have superhuman vision you’ll already start having a hard time seeing the structure.
If you look at analogue B&W film for instance (at least the ones I’m familiar with), each individual crystal is either black or white. But the resolution is so high you don’t perceive it unless you look under a microscope, and if you scan it, you need very high res (or high speed film) to see the grain structure.
Dithering is not an illusion because the shades are actually still there. With the correct algorithms, you could upscale an image, dither it, down res it, and get back the exact same tones. The data isn’t “faked”, it’s just represented in a different way.
If you’re calling it an illusion, you’d have to call pretty much every way we have of representing an image, from digital to analog, an illusion. Fair, but I’d rather reserve the term for when an image is actually misinterpreted.
I would define an illusion as something where your perception of a thing differs from the reality of the thing in a way that matters in the current context. If we were discussing how LCD screens work, I would call the color white an illusion, but if we were discussing whether to make a webpage background white or red, I would not call the color white an illusion.