"ER Physical Local Data store" allows you to describe the store of an application by referencing only a logical data domain.
Since Aquila we have kept only the "Physical local Data Store" on application because it gives the choice of referencing either a logical data domain or relational or physical data domain.
A conversion was provided in Aquila SP1 to migrate old "ER Physical Data Store" stores to "Physical Local Data Store".
"Physical Local Data Store" allows to define data store with different type of data (Physical, Relational...).
But originally we had only Data Store with Entity/Relationship notation/type. We kept it for compatibility reason and it is not activated by default in diagrams (but it is still there and user can activate it in diagram view windows). As we do not have this "hidding" option in property page it is visible today.
In Aquila version it has been rationalized and all data type are now under "Physical Local Data Store".