X-ray phase and dark-field contrast have recently been the source of much attention in the field of X-ray imaging, as they both contribute new imaging signals based on physical principles that differ from conventional X-ray imaging. With a so-called Talbot grating interferometer, both phase-contrast and dark-field images are obtained simultaneously with the conventional attenuation-based X-ray image, providing three complementary image modalities that are intrinsically registered. Whereas the physical contrast mechanisms behind attenuation and phase contrast are well understood, a formalism to describe the dark-field signal is still in progress. In this article, we report on correlative experimental results obtained with a grating interferometer and with small-angle X-ray scattering. Furthermore, we use a proposed model to quantitatively describe the results, which could be of great importance for future clinical and biomedical applications of grating-based X-ray imaging.