The contributions of the correlated and uncorrelated components of the electron-pair density to atomic and molecular intracule I(r) and extracule E(R) densities and its Laplacian functions del(2)I(r) and del(2)E(R) are analyzed at the Hartree-Fock (HF) and configuration interaction (CI) levels of theory. The topologies of the uncorrelated components of these functions can be rationalized in terms of the corresponding one-electron densities. In contrast, by analyzing the correlated components of I(r) and E(R), namely, I-C(r) and E-C(R), the effect of electron Fermi and Coulomb correlation can be assessed at the HF and CI levels of theory. Moreover, the contribution of Coulomb correlation can be isolated by means of difference maps between I-C(r) and E-C(R) distributions calculated at the two levels of theory. As application examples, the He, Ne, and Ar atomic series, the C-2(-2), N-2, O-2(+2) molecular series, and the C2H4 molecule have been investigated. For these atoms and molecules, it is found that Fermi correlation accounts for the main characteristics of I-C(r) and E-C(R), with Coulomb correlation increasing slightly the locality of these functions at the CI level of theory. Furthermore, I-C(r), E-C(R), and the associated Laplacian functions, reveal the short-ranged nature and high isotropy of Fermi and Coulomb correlation in atoms and molecules.