The structure in four racemic fluids is explored using two integral equation theories: the reference interaction site method (RISM) [D. Chandler and H. C. Andersen, J. Chem. Phys. 57, 1930 (1972)] and the diagrammatically correct theory of Chandler, Silbey, and Ladanyi (CSL) [D. Chandler, R. Silbey, and B. M. Ladanyi, Mol. Phys. 46, 1335 (1982)]. Discrimination is measured by comparison of site pair distributions for sites on identical molecules with the corresponding distributions for sites on mirror-image molecules. We find that discrimination is largest for distributions between the smallest sites in the molecules. Between racemates, those consisting of more asymmetrical chiral molecules (i.e., with a bigger range of site sizes and bond lengths) show the largest discrimination. The indirect correlation function is shown to be nondiscriminating in racemates. Further, exact relationships between like-like and like-unlike differences in the other pair functions have been obtained. From these, the importance of the bridge functions in discrimination is evident. The CSL theory always satisfies the exact relationships, even with approximate bridge diagrams. RISM theory cannot satisfy these exact limits regardless of density and closure relation. We have found that RISM theory predicts qualitatively incorrect pair distributions at low densities, but that the difference in the distributions is more accurate. All bridge diagrams which contribute to O(rho (o)) have been enumerated and evaluated. Inclusion of these diagrams into the CSL theory leads to exact results at low density. However, we find that the inclusion of the rho (o) diagrams has dramatically improved the quality of the CSL theory at all densities.