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We show that the kinetic-theoretical self-diffusion coefficient of an atomic fluid plays the same role as the short-time self-diffusion coefficient DS in a colloidal liquid, in the sense that the dynamic properties of the former, at times much longer than the mean free time, and properly scaled with DS, will be indistinguishable from those of a colloidal liquid with the same interaction potential. One important consequence of such dynamic equivalence is that the ratio DL/DS of the long-time to the short-time self-diffusion coefficients must then be the same for both an atomic and a colloidal system characterized by the same inter-particle interactions. This naturally extends to atomic fluids a well-known dynamic criterion for freezing of colloidal liquids (Löwen H. et al., Phys. Rev. Lett., 70 (1993) 1557). We corroborate these predictions by comparing molecular and Brownian dynamics simulations on the hard-sphere system and on other soft-sphere model systems, representative of the "hard-sphere" dynamic universality class. [ABSTRACT FROM AUTHOR]