In this work, a new parameterization for the Statistical Association Fluid Theory for potentials of Variable Range (SAFT-VR) is coupled to the discrete potential theory to represent the thermodynamic properties of several fluids, ranging from molecular liquids to colloidal-like dispersions. In this way, this version of the SAFT-VR approach can be straightforwardly applied to any kind of either simple or complex fluid. In particular, two interaction potentials, namely, the Lennard-Jones and the hard-core attractive Yukawa potentials, are discretized to study the vapor-liquid equilibrium properties of both molecular and complex liquids, respectively. Our results are assessed with Monte Carlo computer simulations and available and accurate theoretical results based on the self-consistent Ornstein-Zernike approximation.