Does all Tibetan Buddhism classify the sutras in the same way? Does all Tibetan Buddhism classify the sutras and sastras in the same way, or do specific schools elevate different Indian etc. texts?

I read about Chinese discussion about panjiao (doctrinal classification), and found it really interesting, especially the systems developed by Tsungmi and Zhyiyi, even if may seem quite dogmatic compared to someone like Wonhyo, who practiced hwajaeng, doctrincal harmony, so that "in his works we do not see the application of the practice of doctrinal classification".

Is there an equivalent in Tibetan Buddhism?
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.