Now if Yahoo is no longer a search engine and it's powered by bing... what's going on here?
The SERPs can be different to a degree. Yahoo manipulates the Bing data. Yahoo takes the Bing data and filters it, perhaps IMO with some off-page data, but I think their filtering is better than the input, resulting in GIGO.
Take a look at Yahoo's research papers [labs.yahoo.com], they're heavy into determining what a page is about by analyzing off-page factors. Yahoo's The Signal [news.yahoo.com], a blog about predicting the outcomes of current events with statistical analysis is pretty interesting. It shows what directions Yahoo is taking in analyzing data.