Before revision:  This point of view reveals that specific types of output (e.g., excluding non-reachability information, excluding the self-distances  ) and the order of enumeration (e.g., sorted by distance,  row-wise w.r.t. the distance matrix) have a huge impact on the complexity of APSD while they appear to have no effect on SSSD. In particular, we show for APSD that enumeration without output restrictions is possible with delay in the order of the average degree.
After revision:  This point of view reveals that specific types of output (e.g., excluding non-reachability information, excluding the self-distances (u, u, 0) ) and the order of enumeration (e.g., sorted by distance, row-wise w.r.t. the distance matrix) have a huge impact on the complexity of APSD while they appear to have no effect on SSSD. In particular, we show for APSD that enumeration without output restrictions is possible with delay in the order of the average degree.