One picture distorts the other, in three physically different ways.
Displacement is the blunt one. The colour of the map is read as a direction and a distance, and the target is fetched from over there instead of from here. It smears.
Refraction treats the map as a surface with hills and valleys, works out which way that surface is sloping, and bends the line of sight the way light bends when it passes into water or glass. That is why it looks like something seen through textured glass rather than something smeared.
Reflection uses the same slope but bounces the line of sight off it instead of letting it through, so the target appears mirrored on the map's surface, the way a picture appears in rippling water.
The difference between the last two is the difference between looking through something and looking at it.