We address a long-standing problem concerning the origin of bosonic excitations that strongly interact with charge carriers. We show that the time-resolved pump-probe experiments are capable of distinguishing between regular bosonic degrees of freedom, e.g., phonons, and the hard-core bosons, e.g., magnons. The ability of phonon degrees of freedom to absorb essentially an unlimited amount of energy renders relaxation dynamics nearly independent of the absorbed energy or fluence. In contrast, the hard core effects pose limits on the density of energy stored in the bosonic subsystems resulting in a substantial dependence of the relaxation time on the fluence and/or excitation energy. Very similar effects can be observed also in a different setup when the system is driven by multiple pulses.