Understanding the dynamics of vortex matter subjected to random and correlated pinning disorders in layered superconductors remains a topic of considerable interest. The dynamical behavior of vortices in these systems shows a rich variety of effects due to many competing interactions. Here, we study the ac response of as-grown as well as heavy-ion-irradiated Tl 2 Ba 2 CaCu 2 O 8 (Tl-2212) thin films by using a micro Hall-probe susceptometer. We find that the dynamics of vortices in the high-temperature, low-field regime of the H -T phase diagram investigated here depends on the nature of pinning defects. While the decay of screening currents J (t) indicates a glassy behavior in both types of samples, the nature of the glassy phase is different in the two cases. Samples with columnar defects show distinct signature of a Bose glass in the measurement of J (t) and the angular dependence of the irreversibility field (B irr ).