I think what this means is that the DB object is the table or index definition in the meta-schema, whereas the storage object is the actual implementation of that definition, i.e. the table or object itself.
Imagine your DB contains a Customer table. That table, which contains customer records, is the storage object which is assigned to a storage area. The definition of the Customer table, which collectively resides in the schema in records in _File, _Field, _StorageObject, etc., is the database object.