Short answers, pulled from the story.
The Tibetan Buddhist canon divides into two collections, the Kangyur and the Tengyur. The Kangyur holds words attributed to the Buddha himself, and the Tengyur holds commentaries, treatises, and abhidharma works by later masters.
The Tibetan Buddhist canon was first translated into Tibetan in the 8th century. That earliest translation effort is known as the Ancient Translation School of the Nyingmas.
Buton Rinchen Drub, who lived from 1290 to 1364, reorganized the Tibetan Buddhist canon in the 14th century. He divided it into the same two categories, Kangyur and Tengyur, still used today.
About a dozen Kangyur editions of the Tibetan Buddhist canon are available today. They include the Derge, Lhasa, Narthang, Cone, Peking, Urga, Phudrak, and Stog Palace versions, each named after where it was printed or copied.
The 39th Tibetan king, khri-lde srong-btsen, also known as sad-na legs-mjing-gyon, ordered the first catalogue of the Tibetan Buddhist canon. He reigned from 776 to 815 and required all translated works to be catalogued, reviewed, and standardized.
The Tengyur section of the Tibetan Buddhist canon contains 3,626 texts across 224 volumes according to its basic division. A separate count from Dharma Publication's edition puts the bsTan-gyur at 3,387 texts across 127,000 folios.