ArcGIS Desktop is a complete suite for desktop GIS that you can use to create maps, perform spatial analysis, and manage data. It includes both ArcGIS Pro and ArcMap.
ArcGIS Pro is Esri’s next-gen 64-bit desktop GIS. Technologically ahead of everything else on the market, ArcGIS Pro provides professional 2D and 3D mapping in an intuitive user interface. You can think of ArcGIS Pro as a big step forward—one that advances visualization, analytics, image processing, data management, and integration.
ArcMap is the industry leading, traditional GIS authoring and editing application.
ArcGIS Desktop is built to work with ArcGIS Online, Esri's cloud-based mapping product, and ArcGIS Enterprise, Esri’s Web GIS mapping platform for your infrastructure.