Note: I listen to Talk Show only occasionally, I'm more of Hypercritical guy.
So, Dan wanted an iOS app for some time now (year? more?) - and he was working with Black Pixel (http://blackpixel.com) on that.
We don't know exactly why, but that app was never released - Dan stopped talking about it (I'm not actually sure about this, somebody please correct me if I'm wrong.). Recently, he (again, not sure) wrote new app - that's what's on App Store as 5by5 app.
Parts of "old" app were apparently reused by Black Pixel while working on Mule Radio app (also by Black Pixel.).
The 5by5 app is a lot more live-listening-focused than the Black Pixel one. The Black Pixel/Mule app is a curated podcasting client. The current 5by5 app is specifically focused on live broadcast/notification/listening. It's an interesting contrast, IMHO; I wish each app had some of the features of the other.
There's only one. 5by5's app is for listening to live broadcasts of shows on their network.
Presumably, they were previously working with BlackPixel to do a podcasting app for the 5by5 shows, which was never released. The Mule Radio app appears to be a re-branded version of that unreleased app.
According to this tweet by Dan Benjamin about adding podcasting to the 5by5 app, he feels other apps already do it better. This may have been the reason why they scuttled their own podcasting app and went with a live broadcast app instead:
