Tuned dynamic absorbers and tuned mass dampers are reactive devices used in structural and acoustic systems to either absorb oscillation at a certain forcing frequency or damp oscillation at a particular resonant frequency, respectively. The make up of tuned absorbers and tuned dampers are for the most part the same, i.e., they are both made up of an inertia element (mass/inertance), a restoring element (spring/compliance), and an energy dissipating element (damper/sound absorbing material). What distinguishes one from the other is the extent of energy dissipation in their dissipative element. Tuned absorbers have negligible but tuned dampers have sizable amount of energy dissipation (damping).
In terms of applications, dynamic absorbers are used to abate the extent of a harmonic perturbation experienced by a structure (or an acoustic environment) and are tuned to the perturbation frequency. Tuned dampers are used to add tuned damping to a single mode of a structure (or a standing wave of an acoustic environment) and as such are tuned to the natural frequency of that mode (standing wave).