The ArcGIS Runtime SDK for .NET and the ArcObjects SDK for .NET are totally different things.
If you want to extent ArcMap in any way, ArcObjects is your choice. Technically, ArcObjects is a COM library with a .NET layer on top to write extensions (or Add-Ins) in .NET.
On the other hand, ArcGIS Runtime SDK for .NET is a complete rewrite to build own standalone applications, mostly to interact with ArcGIS Online or Portal for ArcGIS.