  We focus on two models of nearest-neighbour random walks on d-dimensional
regular hyper-cubic lattices that are usually assumed to be identical - the
discrete-time Polya walk, in which the walker steps at each integer moment of
time, and the Montroll-Weiss continuous-time random walk in which the time
intervals between successive steps are independent, exponentially and
identically distributed random variables with mean 1. We show that while for
symmetric random walks both models indeed lead to identical behaviour in the
long time limit, when there is an external bias they lead to markedly different
behaviour.
