The Link page was curated by the site operator and usually a linear list. IT's main goal was to say "Hey, this is cool, too".
A webring was more like a collective, whereas individual webring members did not necessarily know or agree with every other site in the ring. And it usually was not a list either, but more of a mini topical directory, often with a token-ring-style "Visit the next / random / prev site" navigation you could add to your own page. Webrings were already geared to increasing visitor numbers to your own page ("Others will link to me").
Oh, those were easier times.
In their heyday, there'd also be "start your own webring" sites, so you didn't need cgi-bin access on your GeoShitties or AngelFucker or TriPoop or xoom [1] site in order to start up a webring.
[1] The dry and square history books will claim that the most exciting thing about xoom was its large storage allocation (10mb at launch! 25 soon after! You could upload an entire three minute mp3 at 128CBR "CD-Quality" bitrate and still have tons of space left over for two-frame .gifs!) or its simple members.xoom. com/username URL, but the true soldiers of those bygone battledays will know it was xoom's resiliency to childish renaming-mockery.