It doesn't neccessarly have to be such a "ring" that you navigate from website #1 to website #2 and the order is always the same, and you cannot jump, or even do random browsing.

I think initially the idea was mainly around the "ring" concept, but relatively quickly lots of different implementations did lots of different things, and we still called those "webrings" even though many weren't conceptually "rings" at all, more like "lists of websites that are kind of somewhat about the same thing, sometimes". There was typically a "Random" button/link too, and index, sometimes categories and more.

It can be a list of websites, with random order, the main point is people's websites linking to other people's websites, in some way, that it could eventually circle back somehow, then you have a webring.