  We obtain B\"acklund transformations and integrable time discretization of
the recently introduced deformed Ruijsenaars-Schneider many-body system which
is the dynamical system for poles of elliptic solutions to the Toda lattice
with constraint of type B. We also show that the deformed Ruijsenaars-Schneider
system in discrete time is the dynamical system for poles of elliptic solutions
to the fully discrete Kadomtsev-Petviashvili equation of type B. Besides, we
suggest a field analogue of the deformed Ruijsenaars-Schneider system on a
space-time lattice.
