The Stokes-Einstein (SE) relation is examined for hard-sphere (HS) and Weeks-Chandler-Andersen (WCA) fluids by the molecular dynamics method on temperatures and densities corresponding to the saturated vapor line of Lennard-Jones (LJ) liquids. While the self-diffusion coefficient, D, and shear viscosity, η sv, increases and decreases, respectively, with increasing steepness in interaction potentials, the same SE relation holds for HS and WCA fluids as that obtained for LJ liquids, i.e., Dη sv = (k B T/C)(N/V)1/3, where k B is the Boltzmann constant, T is the temperature, and N is the particle number included in the system volume V. The coefficient C is almost constant at about 6 to 2π for η > 0.3, where η is the packing fraction. The results show that the SE relation for simple liquids and fluids does not need to bear any concepts of both the hydrodynamic particle size and the boundary condition. In light of this SE relation, the Enskog, Eyring-Ree, and Zwanzig theories are quantitatively tested. In addition, the cause of deviation from unity of the exponent in the fractional SE relation for simple fluids is clearly accounted for. The present results show that applying both the original and the fractional SE relations to simple liquids and fluids does not lead to any meaningful discussions.