First of all, this shrinkwrap thread seems like what you’re looking for?
If not, and assuming both objects are 3D meshes (if one is 2D, just use decals) - you can curve any “flat” shape around an arbitrary cylinder / sphere in the vertex shader - example (try modifying “Alpha” in top-right.)
As in lines 103-105 in the codepen - pretty much all you need to do is multiply the vertex position of one axis by sin / cos of a position on another axis.
Alternatively - you can also offset the vertices away from the center of the model - so that the distance between each vertex and the center, on the x/z plane, is equal to the radius of your cylinder.
But the final solution depends on how you prepare the original models - just like in Blender, there’s no single solution that’d fit all types of geometries - you need to test different modifiers / wrap methods / parameter configurations.