Studies of the dynamics of isolated interacting many-body quantum systems are at the forefront of
experimental and theoretical physics. A major open question is the identification of the time scales
involved in the relaxation process of these systems. Using experimental observables and a realistic
interacting many-body quantum system, we unveil three different time scales: a very short time
that characterizes the early decay of the initial state and two much longer time scales that increase
exponentially with system size. These two are the Thouless time, tTh, and the relaxation time, tR.
The Thouless time refers to the point beyond which the dynamics acquires universal features and
relaxation happens when the evolution reaches a stationary state. We show that in chaotic systems,
tTh ≪ tR, while for systems approaching a many-body localized phase, tTh → tR. Our results are
compared with those for random matrices, which corroborates their generality.