We present evidence via molecular simulation that the supercooled fluid states of SPC/E water as well as the "repulsive" and "attractive" supercooled fluid states of a recently introduced model for colloids with short-ranged attractions are characterized by the same functional relationship between self-diffusivity and the pair correlation function. We discuss how this simple relationship connects to an earlier finding that the temperature dependency of a supercooled fluid's single-particle dynamics tracks that of its excess entropy (relative to ideal gas). The generality of this observed structure-property relationship is supported by its ability to successfully describe the nontrivial behaviors of these very different types of model systems.