This paper investigates in a formal context some fundamental controllability properties “from” and “to” the origin of probabilistic discrete-time dynamic systems as well as their uniform versions and complete controllability in a class of probabilistic metric spaces or probabilistic normed spaces, in particular, in probabilistic Menger spaces. Some related approximate probabilistic controllability properties are also investigated for the case when a nominal controllable system is subject to either parametrical perturbations or unmodelled dynamics. In this context, the approximate controllability of a perturbed system is a robustness-type approximate controllability provided that the nominal system is controllable. Some illustrative examples are also given.