The published info. I have says towel bars at 48 inches off the floor is a common height (not a requirement).

For towel rings, I would accommodate the towels you plan to hang, consider how far you have to reach, etc. I find no standard for those. Remember that because of its circular design, towels will hang a little lower on it than they would on a towel bar.

I'm hanging some of my towel BARS, for hand towels, at 22" above the top of the counter, and some at 18". (I like mine higher than usual and we both have long arms.) You want to be able to reach them, so measure up in your current bath and try it out.