Dynamic objects (like StaticMeshComponents and SkeletalMeshComponents with Mobility set to Movable) must integrate into the static shadowing of the world from distance field shadowmaps. This is accomplished with Per Object shadows.
Each movable object creates two dynamic shadows from a stationary light: a shadow to handle the static world casting onto the object, and a shadow to handle the object casting onto the world. With this setup, the only shadowing cost for stationary lights comes from dynamic objects that it affects. This means the cost can vary from very little to a large amount, depending on how many dynamic objects there are. With enough dynamic objects, it is more efficient to use a Movable light instead.
Directional Stationary Lights are special because they support whole scene shadows through Cascaded Shadow Maps at the same time as static shadowing. This is very useful in levels with a lot of animating foliage; you want to have moving shadows around the player but do not want to pay the cost of having many cascades to cover a large view range. The dynamic shadows are faded into static shadows over distance, such that the transition is often indistinguishable. To set this up, just change the Dynamic Shadow Distance StationaryLight of a DirectionalLightStationary to be the range at which you want the fade to happen.
Movable components will still create PerObject shadows even when using Cascaded Shadow Maps on a directional light. This behavior is useful with small Dynamic Shadow Distances, but incurs unnecessary cost with larger distances. To disable PerObject shadows and save performance, disable Use Inset Shadows For Movable Objects on the light