Does all Tibetan Buddhism classify the sutras in the same way?
There are variations in the classification per school/monastery. All schools divide the canon in Kangyur and Tengyur (resp. original canon and treatises). 

The number of Kangyur texts varies. Variations include the Derge, Lhasa, Narthang, Cone, Peking, Urga, Phudrak and Stog Palace versions, each named after the physical location of its compilation.