This article introduces the notion of absolutely distinguishable discrete-time dynamic systems, with particular applicability to linear time-invariant and linear parameter-varying systems. The motivation for this novel type of distinguishability stems, in particular, from the stability and performance requirements of worst-case adaptive control methodologies. The main results presented herein show that, in most practical cases, a persistence of excitation type of condition and a minimum number of iterations are required to properly distinguish two dynamic systems. We also demonstrate that the former constraint can be written as a lower bound on the intensity of the exogenous disturbances. The applicability of the developed theory is illustrated with a set of examples.