A long time ago my Aunt had a printed illustration of a child in rain boots playing in puddles. Altogether the image included puddles, raindrops, rain clouds, the child in rain boots, the splashed water, and an umbrella. The base image included all those things, but standing out from that by a mm or two were the puddles and rain clouds on a duplicate printed layer. Then a few mm above that layer was the child and splashed water, and then finally on the most pronounced layer was the umbrella. There was foam tape/glue that was stacked underneath each layer to give the object an illusion of depth and the raised layers were printed on a thick card stock and sat just over their original print. If you looked at it from the side you could see the duplicate images. It wasn't unbelievable but it was neat.

Does this concept have a name? I've been searching for any hint of a reference with no success. Closest I've found is a "cut out paper" style but that's mostly just colored paper cut into shapes, south park style.