We investigate the terahertz (THz) response of a square antidot superlattice by means of photoconductivity measurements using a Fourier-transform-spectrometer. We detect, spectrally resolved, the cyclotron resonance and the fundamental magnetoplasmon mode of the periodic superlattice. In the dissipative transport regime both resonances are observed in the photoresponse. In the adiabatic transport regime, at integer filling factor ν=2, only the cyclotron resonance is observed. From this we infer that different mechanisms contribute to converting the absorption of THz radiation into photoconductivity in the cyclotron and in the magnetoplasmon resonances. In the dissipative transport regime, heating of the electrons via resonant absorption of the THz radiation in the two-dimensional bulk is the main mechanism of photoconductivity in both resonances. In the case of the cyclotron resonance, and especially in the adiabatic transport regime, we find an additional contribution to photoconductivity which we interpret as being caused by THz-absorption-induced backscattering of edge states. The characteristic decay length of the magnetoplasmon at the sample edges is about an order of magnitude larger than the typical width of the edge states in the quantum Hall effect. The magnetoplasmon is therefore not able to induce such backscattering of edge states. Thus in the adiabatic transport regime, i.e., when only the edge states contribute to electric conduction, magnetoplasmon excitation does not induce a photoconductive signal.