What are three differences between Mennonites and Amish?

There is no difference between the clothing of the Amish and the Mennonite.

There are dozens of plain sects that refer to themselves Amish or Mennonite and still others that call themselves Peachy, Beachy, Apostolic, and other labels, but the clothes worn really depend on the particular congregation one is talking about, as it depends on tradition more than the ordnung, and the ordnung is a living set of rules, rather than a static one.

The textbook answer is that the difference between the Amish and the Mennonite is that the Amish practice shunning and the Mennonite do not. Shunning is the practice of refusing to recognize a member of the church who has varied from the practices of the church in a significant way, has been assisted in conforming, and has continued to live a nonconforming life. That means that having been shunned, one cannot talk with wife, children, brothers and sisters, patents, or the many church members that provide the specialized goods and services needed in ordinary life - quite a burden.

However, the congregations have drifted back and forth, and there are liberal Amish, and conservative Mennonite groups, so there really no useful distinctions between them. I met an Amish woman who came back to Indiana to visit her mother, hospitalized for a heart attack. She was wearing plain white tennis shoes, which were not worn by any of the local Amish congregations, but she had moved to upstate New York, which allowed them.