Mennonites and the Amish are not the same (the Amish are a splinter faith from the Mennonites), though they're similiar. And the only simililarity the three groups have is that we're all Christians and read the Bible (though the Amish try not to quote it too often, as that would be pride).
Differences (though these are generalized, as there are many splinter groups from each):
Shunning--SOME Mennonites and the Amish shun. Mormons do not.
Community--all three groups are big on family and community, but the A. and M. are found only in certain parts of the world (not because those areas are special, but because that's the way it's worked out). Mormons live anywhere and everywhere.
Clothing--all three groups believe in dressing modestly, but Mormons don't do the prairie dress thing. We can wear whatever as long as we're not flashing too much cleavage.
Electronics--A. do not use electricity. Some M. do. All Mormons do.
Military--of the three, only the Mormons can join the military.
Amish and Mennonites are fairly easy to spot (they're the ones in the buggy). Most Mormons aren't. We're not really anything like the A. or M.
Both are idiots, frankly.
Mormons use computers and would be able to see this question.
Mormons believe in the Book of Mormon as well as modern prophets and apostles. They have an open canon of scripture. They are a restored church, and not part of the protestant reformation.
Mennonites do not believe in the Book of Mormon. They do not believe in living prophets and apostles. They have a closed canon of scripture. They are a protestant denomination.
They are miles apart but a sliver of overlap ( that being the Bible). For details go to wikipedia.
Mormons are modern people and have different way of living. Amish live in they community away from how regular American live. Mennonites are something between