When Yahoo and Microsoft joined hands and started working together on search and advertising, the tasks were divided among the two companies. Bing would power Yahoo Search, Yahoo would handle big name ad campaigns and Microsoft would handle the self-serve ad network.
In fact, it's a bit more complicated than that, the ad network technology is supplied by Microsoft, but most of the things people are involved with, support, sales, are handled by Yahoo.
In any case, to make it even clearer that this is a joint effort, Microsoft and Yahoo are doing a rebranding of their common tools.
For one, the search ad network, or marketplace as they call it, will be dubbed the Yahoo Bing Network. Note that Yahoo comes first. The network is used on Yahoo Search, Bing, and a few other places, notably Facebook, but also Amazon and others.
As part of the rebranding, Microsoft's adCenter becomes Bing Ads. Along with the new name, advertisers will also be getting a few new features and updates, though the core product remains the same.