'As stored' is a static configuration, it cannot be changed or synchronized as it defines a point in history. Think of it as baselines which are applied to individual assemblies and drawings. It is just saying on an item by item basis, when version of x of the drawing was checked in, what was the version(s) of the model(s) used to make the drawing. Or when version x of the assembly what checked in, what were the versions of the assembly members.
Latest on the other hand is a dynamic every changing configuration.