Buddhism can be divided into two major traditions - Theravada ("the view of the elders") and Mahayana ("the greater vehicle"). Both of these schools originate in South Asia, but only Mahayana became prevalent in East Asia. Within the Mahayana tradition there is also the Vajrayana ("diamond" or "thunderbolt vehicle") tradition, also called "esoteric" or "tantric" Buddhism. This form of Buddhism is also originally from India and today is most prevalent in Tibet and surrounding regions, but does find its way to Japan as well in the form of Shingon.
Below is a guide demonstrating the major schools of Buddhism that are relevant to Japanese history. Most of the words have links to relevant articles on Britannica Academic if you would like more information (Columbia College login is required).