I think the history is that at some point, people in China began to hear of "Buddhism".
From China it eventually moved/migrated to Japan (where it's called "Zen"). There were/are several schools or sects in Japan. My (not well-informed) impression is that an emphasis on meditation (or "sitting") might be partly in reaction/opposition to sectarian arguing over doctrine and intellectualisation.
As well as Japan, Zen also exists in Korea and Vietnam.
Some of the first Buddhists to arrive in the USA were Zen school, and "Zen" might be better known (I don't mean "well known", but known in the sense that "a lot of people will have at least heard of it") in Western popular culture than, for example, Theravada.
For example among the popular books on Zen that I read quite a while ago, The Three Pillars of Zen and Zen Flesh Zen Bones (both of which helped to popularize Japanese Zen).
One of the popular foundations in the West at the moment is Plum Village whose founder is, I read, from Vietnamese Zen.
And to try to begin to answer "Why is it called Buddhism?" there's Lineage and Dharma transmission .
I think that in theory or traditionally that's understood as an unbroken chain of transmission of Dharma from teacher to student, a chain going back to the earliest teachers and the Buddha himself. The historical reality might be more complicated than that. Even so I think there's an emphasis on studying with (learning from) a living and relatively enlightened teacher, perhaps instead of an emphasis (or an exclusive emphasis) on studying the earliest texts (e.g. the Pali suttas or the Chinese Agamas).
As well as suttas there's also the Vinaya which (I read) is apparently followed within some schools of Zen and not others.