Amish is a sub-category of Mennonite. Here is how the whole hierarchy works:
The largest group is the Anabaptists (http://en.wikipedia.org/wiki/Anabaptist), who are Christians who believe that adult baptism is a necessity because people must make their own choice for Christ - infant baptism, in their view, does not make one a Christian. Most also hold that the Sermon on the Mount is to be taken as literally as possible, and is central to Christian Faith. This makes them pacifist, and Anabaptist churches are sometimes grouped with the Quakers as Peace Churches.
These days, most Anabaptists are Mennonites (http://en.wikipedia.org/wiki/Mennonite). The Mennonites are Anabaptists who follow the teachings of Menno Simons (1496–1561).
Later, in 1693, there was a schism in the Swiss Mennonite church. The issue was shunning, the practice of social isolation of Mennonites who do not follow the rules of the Mennonite order. Followers of Jakob Ammann. Followers of Amman became known as Amish (http://en.wikipedia.org/wiki/Amish_%28disambiguati... http://en.wikipedia.org/wiki/Amish ).
Old Order Mennonites and Old Order Amish dress in older European styles of dress and do not use, or limit the use of, modern technology such as electricity and telephones. However, there are several sub-groups of Christian religious Mennonites and Amish who do dress more to today's conventions and do use technology. In addition, Amish is also an ethnic group, so those who live in modern ways and are not part of the Amish faith may still consider themselves culturally Amish.
The largest group of Amish settled from Germany and German-speaking Switzerland in Pennsylvania. The German word for "German" is "Deutsch." These people became known as the Pennsylvania Dutch or Pennsylvania Germans. They are also settled in Indiana, and new settlements are growing further west in the US.