Google website backlinks and Yahoo backlinks are “similar” but not all the same.
It’s easier to break it up into categories.
On the first category you have a Backlink, just a link on a site which directs to your site.
On the second category you have a dofollow link, a link which will be picked up by all search engines.
On the third category you have a nofollow link, a link which will not be picked up by some search engines.
Google picks up dofollow backlinks only, yahoo picks up both.