I have used rice paper in the past without any issues but the paper did not dissolve on the last cake I did. Does anyone have any ideas on why that might have happened. Thank you.

Well, it's not supposed to dissolve.

Icing sheets dissolve/meld onto icing, but not wafer paper.

I made the same assumption. I have used icing sheets many times and love love love the results, but I bought several cupcake rounds that were printed on rice paper. I made the assumption that they were one and the same. When the cupcake rounds arrived, I was shocked to see how thick (like thin sheets of styrofoam) the rice paper was. It did not dissolve and was a total waste of money. I can't figure out why anyone would want to use rice paper and why they would bother marketing such an unappealing product.

It would be great of rice and/or potato sheets worked due to their price point, but unfortunately it just doesnt give the same results as icing sheets.