Besides their common historical roots, Mennonite and Amish groups all stress that they should live out their beliefs in daily life. While the groups agree on basic Christian doctrine, their differences come in interpreting how those practices should be lived out.
The original difference in opinion came in 1693, when Jacob Ammann, a Swiss Anabaptist leader, felt that the church leaders were not holding to strict separation from the world and that spiritual renewal was needed. Ammann did not believe that the ban, or shunning, was being practiced as it should be. He separated from the Swiss Brethren segment of the Anabaptists over this issue and his followers were nicknamed “Amish.”
Ammann enforced more separatist ways upon his followers, and today some practices among the Amish include: untrimmed beards and hooks and eyes in place of buttons on outer garments of the men; horse and buggy transportation; horse-drawn implements for farming; plain and distinctive dress patterns; no electricity in homes.
However, most contemporary Mennonites are not outwardly that different from any person you meet on the street, and in fact live in countries around the world with a wide variety of ethnic backgrounds. Mennonites believe in simple living, but express that simplicity in a spirit of stewardship and awareness of the needs of others rather than completely separating from society as the Amish continue to do.
The above information was gathered from Anabaptist World USA and other resources. See the MennoMedia store for a booklet called The Amish by John Hostetler, and The Amish: Why They Enchant Us, by Donald B. Kraybill. The Amish in Northern Indiana site provides additional information about the Amish. The web site, How Stuff Works, also has an excellent section on the Amish.