Previously, the Apply to each object separately checkbox had no effect for the Move tab. Now, if several objects are selected, this checkbox is on, and "Relative move" is on, each object is shifted relative to the closest selected object on the left (for X) or below (for Y).
For example, if you have a horizontal row of objects and you move them relatively by X=5px with "Apply to each object separately" on, the leftmost object will shift by 5px, the next one to the right by 10px, and so on; the rightmost selected object is displaced by 5*n px where n is the number of selected objects. As a result, the distance in each pair of adjacent objects will increase by 5px and the whole row will be spaced out, much like a letterspacing adjustment spaces out a text string. Moving these objects by X=-5px will, conversely, squeeze them tighter together: the leftmost will move by -5px, the next one by -10px, and so on. For Y, the effect is the same except that the move starts from the object closest to the bottom (i.e. with smallest Y coordinate).
When determining the order of shifting objects, for X, the left edges of their bounding boxes are sorted horizontally, and for Y, the bottoms of their bounding boxes are sorted vertically. Order of selecting the objects or z-order does not matter.