I have called these Bark Rings because the surface texture looks somewhat like tree bark.
The larger of the two was the first attempt, I wanted to experiment with both surface textures and curving the sides of a ring in. I learnt a thing or two from this and used the new found knowledge to make the second one as a birthday present for my sister.
I like the final surface texture on the thiner banded ring better, the second one I made, it is far closer to the actual effect I was aiming for in the initial experiment.