Atom interferometers with long baselines are envisioned to complement the ongoing search for dark matter. They rely on atomic manipulation based on internal (clock) transitions or state-preserving atomic diffraction. Principally, dark matter can act on the internal as well as the external degrees of freedom to both of which atom interferometers are susceptible. We, therefore, study in this contribution the effects of dark matter on the internal atomic structure and the atom's motion. In particular, we show that the atomic transition frequency depends on the mean coupling and the differential coupling of the involved states to dark matter, scaling with the unperturbed atomic transition frequency and the Compton frequency, respectively. The differential coupling is only of relevance when internal states change, which makes detectors, e.g., based on single-photon transitions sensitive to both coupling parameters. For sensors generated by state-preserving diffraction mechanisms like Bragg diffraction, the mean coupling modifies only the motion of the atom as the dominant contribution. Finally, we compare both effects observed in terrestrial dark-matter detectors.