In the ESRI UC 2016 Q&A that is online here, I found this little tidbit about what are the product names:
Several years ago, as part of the naming standards issue, we changed the names to be consistent with ArcGIS for Server and ArcGIS for Desktop, etc. What we found is that we made a mistake, and that our users are more comfortable referring to these products as ArcGIS Server and ArcGIS Desktop, so starting now ESRI is changing these names back to ArcGIS Desktop and ArcGIS Server.
These changes will be implemented on our website and in the software over the next release cycles.
All us old timers rejoice! 🙂