What term describes the displacement between one level and the level above or below?

The term that correctly describes the displacement between one level and the level above or below is "story drift." This concept is particularly significant in the context of structural engineering and building design, where it refers to the lateral displacement that occurs between different levels of a structure during events such as seismic activity or high winds. Story drift is critical when assessing the integrity and performance of a building under such conditions, as excessive drift can lead to structural weaknesses or failure.

Other terms provided in the choices have specific meanings that do not accurately capture this concept. For instance, "vertical shift" might imply a change in vertical position but does not specifically reference the displacement between two levels in a structural context. "Level offset" could suggest a difference in elevation but lacks the connotation of horizontal displacement during lateral forces. Similarly, "height differential" generally refers to the difference in height between two points and is not typically used to describe the lateral movement or displacement between building levels, which is the essence of story drift. Thus, story drift is the most precise term to describe the moving relationship between floors in a building during seismic events or other forces.