Contact regions are used to define surfaces that can come into contact with one another between different components in an assembly due to applied loads and/or motion. Contact region analysis uses non-linear solutions because the contact pressure and area are not directly proportional to applied load. Contact regions also have options that allow you to specify number of intervals (to graph contact pressure as a function of load) and localized mesh refinement (change the mesh as the surfaces come into contact). Contact regions can also be applied to components that have interference fits and can be used to simulate drop tests.
Interfaces are used to change the mesh between components that are mated or touching in an assembly. By default, if two surfaces of two components are coincident with one another, when Mechanica generates the mesh, the nodes are combined. By using an interface, you can prevent the nodes from being combined. It's all about how you want to simulate forces and displacements from being transferred from one component to another.
Dave Martin