  In a previous paper it was shown that the recently constructed action for
open superstring field theory based on $A_\infty$ algebras can be re-written in
Wess-Zumino-Witten-like form, thus establishing its relation to Berkovits' open
superstring field theory. In this paper we explain the relation between these
two theories from a different perspective which emphasizes the small Hilbert
space, and in particular the relation between the $A_\infty$ structures on both
sides.
