Without going to deep into doctrines, here's a brief historical sketch:
In general, Theravada Buddhist are a doctrinally-conservative group who follow a trend of Buddhism that recommends a withdrawn life of monasticism. Monks and nuns are typically separated like the Catholic Church. It's sort of like ... if the only expression of the Catholic tradition were the Desert Fathers who withdrew into contemplation. This form is found predominately in Sri Lanka, and Southeast Asia, where Buddhism first spread under Emperor Ashoka.
Mahayana Buddhism is sort of our "Protestant" catch-phrase for everything from deity-worshipping Chinese Buddhists (Buddhism processed through Confucianism, among other philosophies, and Taoism) to Zen Buddhism (Buddhism processed through Taoism and Shinto) in Japan. Depending on your preferred scholar, we may also group Tibetan Buddhism into the group of Mahayana, though, it often gets its own designation.
Vajrayana, Tibetan, or Tantric Buddhism is what American teenagers were admiring in the 1960s, when they weren't stuck on the International Society for Krishna Consciousness (see: "Tomorrow Never Knows" by the Beatles for an example of Tibetan Buddhism). This form is highly related to early Indian Buddhism, and was the first form of Buddhism to migrate Northward. This form later influenced Mongolian Buddhism (Tantra processed through Tengriism).
Then we have, what I'll personally call, our "Western Buddhism". While "Western" is a poor adjective to describe anything in comparative cultural studies, I think we'll find a markedly different version of Buddhism that was evangelized through modern market economies to consumer societies that offer a highly eclectic form of Buddhism. I almost want to call it Eclecticism instead of Buddhism, and Siddhartha's teachings aren't as important as later Buddhist scholars.