TWO MAJOR BRANCHES~
THERAVADA~ ("the elder's way") the oldest branch surviving, they emphasize the important of reaching enlightment for oneself. They source "the Pali canon" of texts and use terms in Pali. Vipassana meditation is a main practice.
MAHAYANA~ ("the greater vehicle") The broadest branch, this includes many diverse schools of Buddhism, including Zen, Vajrayana and more. The unifying element is the teaching of Bodichitta- the Bodhisattva vow: cultivating one's enlightenment not just for oneself, but out of devotion to the well-being of all others. There are source writings in Sanskrit and in vernacular languages in each coutry, perhaps especially in Japanese.
VAJRAYANA BUDDHISM: Tibetan Buddhism, of which His Holiness the Dalai Lama is the head. Tibetan Buddhism uses various unique meditation techniques, including visualizations, prayer wheels, calm abiding (very similar to vipassana) and more. There is a merging between the indigenous beliefs and worldview (Bon) and Buddhism, which results in a very rich, unique form of living practice.
ZEN BUDDHISM: mainly thought of as a Japanese school, there are Zen schools in China (where its called Chan), Vietnam and other Buddhist countries. Zen is known for its paring down of everything to its simplest form. Its main practice is mindfulness. Seated and walking meditation are used, along with verses, stories and riddles to help the mind come deeply into the here and now. Zen practitioners generally spend a lot of time meditating on the cushion.
ENGAGED BUDDHISM: Thich Nhat Hanh, actually a Vietnamese Zen monk, founded Engaged Buddhism (and monks order of Interbeing) during the Vietnam War to help encourage monks, nuns and lay practitioners to take there practice beyond the meditation hall to be peace and share peace as compassionate activists. Thay (Vietnamese for teacher), encourages mindfulness practiced equally in all moments, not just on the cushion. This is a Zen teaching, but Thay seems to make it even more practical and accessible for the lay person.
NICHIREN BUDDHISM: a Japanese school of Buddhism based on Nichiren, a Buddhist reformer. This schools focuses on studying the Lotus Sutra as the Buddha's ultimate teaching, chanting the Lotus Sutra, and its title in Japanese (namo myoho renge kyo) in front of a special altar (the gohonzon) representative of the journey to Buddhahood.
There are many other schools, but these are some of the main ones you will encounter. Following what intrigues you, you can look deeper into that which resonates for you. This way you may find inspiring practices to serve and uplift your life.