There are other posting that address this question. Do a search on the forum. In short, RBE2 is a rigid element which adds stiffness. RBE3 is an interpolation element used to distribute mass and loads. It can also be used transition elements types (shells to solids, beams to solids, etc.) and Hypermesh uses them in one of their spot weld generation utilities. Many uses but do not use them unless you understand them.
RBE2 adds infinite stiffness to attached nodes which means both nodes to exactly the same displacement whereas RBE3 is an interpolation element and distributes the loads and the mass depending on the length. Depending on the application one of these rigid elements should be used.
Assume you have a plate with a rigid box attached to it by 4 screws. Using the location of center of mas of the box you place a node there, apply downward force (weight), other applied forces, and run it.
You use RBE2 in this case because the box adds stiffness to the body, but you do not want/need to model the box.
You are both correct in part and its the terms that you are using to describe it that are confusing things.
The RBE2 is a rigid connection typically attaching a single node to other multiple nodes. Depending on what DOFs you are transmitting (translations and/or rotations) you are slaving those nodes to the single master. If you consider just translations (to be simple) then the slave nodes will have the same displacements as the master. There will be no relative displacement between the slaves. Does this change the stiffness ? Well it sure does if you look at the nodes that have no relative displacement (slaves and master alike).
