If you're wondering which group is allowed to drive cars and which uses horse-drawn buggies, it's not that easy. The Mennonites and Amish have a common ancestor in a group called the Anabaptists, a Christian movement that began in Europe around the time of the Reformation. Like all Protestants, the Anabaptists believe in Jesus Christ and place great emphasis on the Bible. In addition, the original Anabaptist doctrine called for a total, voluntary commitment to God expressed through adult baptism, pacifism, a plain appearance, and a direct connection between people and God.
In 1536, Menno Simons, a Dutch Catholic priest, gathered the scattered Anabaptists of Northern Europe into congregations, earning the movement the "Mennonite" moniker. In 1693, a Swiss bishop named Jacob Amman broke from the Mennonite church, challenging the movement for straying from the original teachings, and established the more austere Amish movement. Both groups fled Europe because of religious persecution and established colonies in Pennsylvania, upstate New York, and Ohio.
There are now a number of sects within the Amish and Mennonite movements, from the very conservative Old Order Amish to progressive Mennonites. The differences between the various groups involve their interpretations of the Bible, the way they use modern technology, the values they place on education, their uses of English, and their degrees of interaction with outsiders. While it's true that Old Order Amish do not use electricity or attend public schools and that progressive Amish and Mennonites do, each church district decides for itself what technological innovations it will and will not incorporate into its lifestyle.
