The version. Seems like the name changes every couple of years.
ArcGIS Desktop is 10.4.x and prior (down to 10.1 I think) 10.5.0+
ArcGIS for Desktop is 10.5.0+ 10.4.x and prior (down to 10.1 I think)
Corrected per Jayanta Poddar 's catch. I looked, but then typoe'd (ugh). You can see this info on the download page in the version pulldown list btw.
(geonet burped...hope this edit makes in thru this time)