That depends what you mean by illusion. A heat mirage, which is a shiny patch floating just above the ground, is not an illusion -- in the sense that your eyes are really receiving light from a weird floaty shiny area just above the ground, and we can describe the physics that causes them to occur.

On the other hand, a heat mirage is an illusion in the sense that, if you go over and look for a reflective object, say a pool of water, at the location of the mirage, you'll find there's nothing there.

The moon illusion, unlike a mirage, is an illusion in that first, stronger, sense, but it didn't have to be. The image of the moon can change size in reality (for example, when viewed through a lens) without affecting the size of the actual moon.

Or just getting further away, or closer.

I just kept thinking my memory was poor since I knew the distance didn't change that much.