I have a problem $A$ which was shown to be PSPACE-complete by reduction from planning. However, $A$ can also be transformed into reachability problem which is NL-complete.
I know that $NL=NSPACE(log \ n)$ and $PSPACE=NSPACE$.
Does this mean $A$ is also NL-complete? IF yes, does it make any difference in this context to say whether $A$ is PSPACE-complete or NL-complete ?