Unreal Engine 4 uses two primary types of meshes, skeletal and static. Skeletal meshes are used for animation and deforming whereas static meshes are not.
Static meshes are meshes that do not have a bone system set-up. Although static meshes do not require bones, the topology and transformations in-engine can be modified through a variety of methods, predominantly materials and particles effects.
Skeletal meshes are rigged using a bone system. When imported into Unreal Engine, a skeletal mesh needs to be set to import the skeleton (bones) and animation (if any). Unreal Engine recognizes the dependencies set-up in a 3d software package, and thus will recognize a simple set-up such as 3DS Max’s dummy objects as bones if the mesh is skinned to those objects.
Skeletal meshes are used for characters, doors, and other objects that require movement and/or easy modification.
*Note: A modular skeletal rig may be more complex than it’s basic form so long as all of the basic aspects of the skeleton exists as part of the more complex version. (double check this)
A collision mesh is a manifold (water tight) mesh that has the explicit purpose of determining collision interactions in Unreal Engine. Once a static or skeletal mesh has been imported into Unreal Engine, the user may go into that mesh's details and select which type of collision mesh they would prefer be used, and Unreal Engine will automatically generate a collision mesh.
Custom collision meshes may be authored in any 3D content authoring software (e.g., Maya or 3DS Max). So long as the file/mesh has a name beginning with "UCX_" followed by the mesh name, it will register as a collision mesh once imported and may be selected in the options of the static or skeletal mesh. In this manner, collision meshes may be added to highly complex objects (e.g., robots) that are less complex then the static or skeletal mesh, or to very simple objects like a plane (e.g., a collision mesh would be a box so that it is watertight with a height of 0 to accurately portray the bounding box of the plane).