This paper aims to address the robust convergence problem that arises from discrete-time iterative learning control (ILC) systems subject to random disturbances. Two alternative approaches are considered in order to achieve the perfect output tracking of the stochastic discrete-time ILC systems in the sense of both expectation and variance, which use the tracking error and the input error for analysis, respectively. It is shown that the convergence results of two approaches to ILC can be established by developing some statistical expressions in super-vector forms. Moreover, it is demonstrated that the convergence results of two approaches to ILC are not always equal, and they can keep the same only in the case where the controlled plants are square.