Your engagement ring can be your wedding ring, if you want. There's not really any specific criteria for what either ring looks like, either. An engagement ring is only really taggable by context, otherwise it would just get tagged ring or wedding ring.
As for the BURs…
In the case of the first, I don't get the removal of implication of wedding ring, to ring. All wedding rings, are rings, after all.
As for the second, I don't get the mechanics of it, so I can't comment.
Wedding bands are a (plain) type of wedding ring, certainly. Tagging "non-band" wedding rings, as wedding ring and ornate ring (and all of them, as ring), makes sense to me.
Tagging them as ornate rings, [/i]instead[/u] of wedding ring, however…
There are tons of ornate rings, that aren't wedding rings. There is a big difference between an ornate wedding ring, and an ornate ring, that isn't a wedding ring. (if it isn't clear which it is, from the image/context, then the image should, of course, only be tagged with ornate ring)