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The diffusion and low frequency vibrational motions of atoms and molecules on surfaces can be measured by means of quasielastic helium atom scattering. In this paper, we discuss and investigate different analytical approximations, based on the theory of stochastic processes, to the dynamic structure factor, considering the two motions on an equal footing. Special emphasis is put on the nature of the corresponding lineshapes, explained in terms of the motional narrowing effect. We also discuss the influence of the diffusional and vibrational coupling and several ways of experimentally separating the two types of contributions to the dynamic structure factor. In particular, we propose that the so-called inelastic focusing singularity from atom–surface scattering controls the lineshapes of quasielastic and vibrational peaks.