Hi,
The new ArcGIS Professional App is the next generation of ArcGIS for Desktop and is an out-of-the-box, end-user GIS application.
The new ArcGIS Runtime SDK for .NET is, as you summarized, a developer SDK based on .NET 4.5, extensively uses the new Task-based async functionality of .NET 4.5, and supports development in Visual Studio 2012.
I hope that clarifies the role of the two products.
Cheers