Stationary Lights are lights that are intended to stay in one position, but are able to change in other ways, such as their brightness and color. This is the primary way in which they differ from Static Lights, which cannot change in any way during gameplay. However, it should be noted that runtime changes to brightness only affect the direct lighting. Indirect (bounced) lighting, since it is pre-calculated by Lightmass, will not change.
Of the three light mobilities, Stationary lights tend to have the highest quality, medium mutability, and medium performance cost.