When Microsoft failed to purchase Yahoo to $47.5bn billion in 2008, they reached a 10-year deal in 2009 for Yahoo to use Bing's infrastructure and "backend" for search [1]. Yahoo provides their own UI/UX and Microsoft provides the actual data.
So, technically, Firefox will be showing very similar (if not identical) results to Bing.
Yahoo has used Bing's search infrastructure for awhile but they've kept the independent front-end and, based on my logs, some level of crawling, presumably to keep their options open so they could switch in the future.
I think yahoo is/was sending off search results to Bing. A long time ago they used to send them to Google. Before that they would refer to themselves as a web directory, not a search engine. And WAYY before that every result page had a link to search on different sites, web crawler, lycos, maybe even google my memory is kind of fuzzy.
The point is that Yahoo cares more about getting people to their portal, not so much what technology it happens to be using.
