This is the best graphic I could find on the branches of Buddhism. You can get a sense of just how much diversity exists within Buddhism, to the point that it may not even be helpful to talk about "Buddhism," but rather "Buddhisms."
From what I understand, Theravada, sometimes called "the Way of The Elders," is the most conservative branch, and strives more than the others to follow every rule and every teaching of the Buddha strictly as found in the Pali Canon. "Western Buddhism" draws mostly from the Theravada tradition. Mahayana, sometimes called "the Great Vehicle," is the most liberal of the branches, being freely combined with other philosophies such as Confucianism and Taoism and even adding unique Buddhist texts, creating "hybrid schools." In general, there is less stress on following the Buddha's teachings strictly and more openness to new developments in Mahayana schools. Vajrayana, sometimes called the Thunderbolt Vehicle, is a smaller branch and is focused on ritual and tantras/mantras. Tibetan Buddhism is probably the most well known modern expression of Vajrayana.
Zen stands out as a "sub-branch" which is also familiar to Westerners. I have heard Zen referred to as "Buddhism gone to China," and also as a fusion of Buddhism and Taoism. There are, of course, sub-divisions of Zen as well.
The branches of Buddhism seem to me far more diverse than the major branches of Christianity. When studying a particular Buddhist teaching, it is important to know which type of Buddhism you are engaging.
This will end the extended series on the Four Noble Truths and Eightfold Path of Buddhism.