The Vinaya Pitaka holds the rules of the monastic order, each framed as a case history: an incident occurs, a complaint reaches the Buddha, a rule is laid down. Read as legal material it is unusually candid about the misbehaviour that prompted it. The Sutta Pitaka holds the discourses, divided into five collections or nikayas, long discourses, middle-length discourses, discourses grouped by topic, discourses grouped by number, and a miscellany, the Khuddaka Nikaya, which gathered the verse anthologies including the Dhammapada and the Jataka birth stories. The Abhidhamma Pitaka is later and different in kind: not narrative at all but a systematic taxonomy of mental and physical events, the technical foundation of Theravada psychology.
That threefold shape is where the name stops being straightforward. Tripitaka describes an arrangement, and the Buddhist canons that use it do not contain the same texts. The Pali Canon is the scripture of Theravada, dominant in Sri Lanka, Burma, Thailand, Laos and Cambodia. The Chinese canon, printed in its standard twentieth-century Taisho edition in a hundred volumes, includes translations of discourse collections parallel to the Pali nikayas, the Agamas, rendered from Sanskrit and Prakrit originals now largely lost, but adds the whole Mahayana sutra literature, several complete Vinayas from different Indian schools, and Chinese commentary and history. The Tibetan canon is split by authorship rather than by basket: the Kangyur, the translated word of the Buddha, runs to around a hundred volumes in the Derge edition, and the Tengyur, translated Indian treatises and commentaries, to about two hundred more. A reader told that Buddhists have a Tripitaka, and picturing one book, has the scale wrong by two orders of magnitude.