My Old Order Amish relatives in Middlefield, Ohio would look like I was crazy if I said something like that to them. They would never ever claim to be Mennonites in any way, shape or form. Mennonites are as English as anyone with the partial exception of clothes and a cap and even then, the Mennonites clothes are more modern. As time goes on, the difference widens. There are some Mennonites you would never know it unless they told you.
I have been wrong before. But I think they they both developed from the teachings of Menno Simons.