BIBO Stability in Z-domain

I'd really appreciate it if someone could please explain to me the condition for a LTI system to be BIBO stable, in z-domain.

I have a background in control, and in linear control for example, if we have the transfer function, we simply look at the poles. But in digital signal processing, sometime we look at the poles - they should be inside the unit circle in order to have BIBO stability - and soemtimes the professor says it depends on the ROC - ROC should include the unit circle -.

I am really confused. Could someone please explain to me the difference?

There is no principal difference between continuous-time and discrete-time systems when judging stability. The imaginary axis of the $$s$$-plane corresponds to the unit circle in the $$z$$-plane, and the region inside the unit circle in the $$z$$-plane corresponds to the left half-plane of the the $$s$$-plane. In both cases the region of convergence (ROC) is essential. Given only the pole locations, you generally cannot say whether a system is stable or not, unless the poles are on the imaginary axis (the unit circle), in which case the system is unstable. In the general case you need additional information, and that information is given by the ROC. Information about the ROC can also be given in the form of a causality constraint, which basically tells you that the ROC is a right half-plane, or - in discrete time - the region outside the pole with the largest radius.