Pure Land is a current before it is an institution. Devotion to Amitabha runs through Chinese Buddhism generally rather than being confined to a school, and the great Chinese figures (Tanluan, Daochuo and Shandao, between the sixth and seventh centuries), systematised a practice that monks of other affiliations also performed. Japan is where it became a set of separate institutions.
Honen, who died in 1212, taught the exclusive nembutsu: that recitation alone suffices and the other practices may be set aside. That was radical enough to get him exiled. His Jodo-shu survives, in Chinzei and Seizan branches. Shinran, his student, founded what became Jodo Shinshu, the largest Buddhist body in Japan. Smaller lines, Yuzu Nembutsu, Ji-shu, continue.
The tradition's largest institutional division was not doctrinal at all. In 1602 Tokugawa Ieyasu, dealing with an organisation whose congregational leagues had fought armies and held provinces for a century, divided the Hongan-ji: Nishi Hongan-ji under Junnyo, and Higashi Hongan-ji established for his brother Kyonyo. Splitting it made it governable. The two have remained separate ever since, as the Honganji-ha and the Otani-ha. It is one of the clearest cases anywhere of a religious division engineered by a state for reasons of public order rather than of belief.
Pure Land's doctrinal quarrels have generally circled one point: whether the recitation is something the practitioner does, in which case its quality and its quantity matter, or something that happens in a practitioner who has already been grasped, in which case neither does.