  We present particular solutions of the discrete Painlev\'e III
(d-P$\rm_{III}$) equation of rational and special function (Bessel) type. These
solutions allow us to establish a close parallel between this discrete equation
and its continuous counterpart. Moreover, we propose an alternate form for
d-P$\rm_{III}$ and confirm its integrability by explicitly deriving its Lax
pair.
