Recently it has been argued that the fluctuations of the order parameter of a system undergoing a second order transition, when considered as a time series, possess characteristic nonstochastic patterns at the critical point. These patterns can be described by a unimodal intermittent map (critical map) and are clearly distinguished from colored noise. In the present work we extend the method introduced in [Y. F. Contoyiannis, F. K. Diakonos, and A. Malakis, Phys. Rev. Lett. 89, 035701 (2002)], in order to reveal universal properties in the deformation of the dynamics of the order parameter fluctuations when departing from the critical point. We show that the obtained systematic change in the order parameter fluctuation pattern can be observed in the critical region of thermal critical systems such as the mean field and the 3D Ising model. In addition, we consider the case of order parameter fluctuations near a tricritical point and we derive an associated characteristic deterministic behavior. A corresponding analysis in the Z(3) model confirms our results. Thus, the method of critical fluctuations introduced previously and generalized here, provides us with a classification scheme allowing for the characterization of temporal fluctuations in an observed time series in terms of critical phenomena.