Usually frosting sheets are made of tapioca starch and have sugar added to them so they stick better (they are also flexible and opaque). Wafer paper is usually made with potato starch and has no sugar, so it sticks less well and is more see-through than frosting sheets. And rice paper is the sheerest and most fragile of all, usually made with rice (though NOT always; I've used some very sheer paper sold as "rice paper" that is actually made with tapioca starch and no sugar).
It could be you got a frosting sheet with very little sugar in it, so it's not so sticky. I would insist on reading/knowing the ingredients, because small variations can cause edible papers to handle so very differently.
I look forward to seeing the picture.