Using correlation plots of binding energy and electron density at the bond critical point, we investigated the nature of intermolecular non-covalent bonds (D-X⋯A, where D = O/S/F/Cl/Br/H, mostly, X = main group elements (except noble gases), A = H2O, NH3, H2S, PH3, HCHO, C2H4, HCN, CO, CH3OH, and CH3OCH3). The binding energies were calculated at the MP2 level of theory, followed by Atoms in Molecules (AIM) analysis of the ab initio wave functions to obtain the electron density at the bond critical point (BCP). For each non-covalent bond, the slopes of the binding energy versus electron density plot have been determined. Based on their slopes, non-covalent bonds are classified as non-covalent bond closed-shell (NCB-C) or non-covalent bond shared-shell (NCB-S). Intriguingly, extrapolating the slopes of the NCB-C and NCB-S cases leads to intramolecular "ionic" and "covalent" bonding regimes, establishing a link between such intermolecular non-covalent and intramolecular chemical bonds. With this new classification, hydrogen bonds and other non-covalent bonds formed by a main-group atom in a covalent molecule are classified as NCB-S. Atoms found in ionic molecules generally form NCB-C type bonds, with the exception of carbon which also forms NCB-C type bonds. Molecules with a tetravalent carbon do behave like ions in ionic molecules such as NaCl and interact with other molecules through NCB-C type bonds. As with the chemical bonds, there are some non-covalent bonds that are intermediate cases.