The effects of the ratio of particle diameter to lattice spacing, zeta, on critical parameters for both polar and nonpolar fluids have been examined in detail. Nonpolar systems studied have short range Buckingham exponential-6 interactions, while polar systems have long range Coulombic forces treated with Ewald summation. Monte Carlo simulations in the grand canonical ensemble combined with histogram reweighting and mixed field finite size scaling have been used. Both critical temperature and critical density decrease on increasing zeta. The critical temperature scales as 1/zeta(alpha) where the exponent was obtained as alpha = (6+/-2) for the nonpolar and alpha = (2+/-0.5) for the polar fluids. The large difference in alpha values between nonpolar and polar fluids results from a much weaker effect of discretization on the critical parameters of nonpolar fluids. (C) 2003 American Institute of Physics.