The existence of one-electron B-B σ bonds, for two different sets of compounds, was investigated by analyzing their electron density with different tools, namely QTAIM, ELF, NCIPLOT, and NBO approaches. Our results indicate that although the generic label "one-electron sigma bond" is often used in the literature, the nature of these bonds varies considerably, or they even do not exist. The [B2 X6 ](-) radical anions give place to true covalent one-electron σ bonds, the stronger the more electronegative is the X substituent. When both boron atoms are substituents in a rigid aromatic moiety, such as naphthalene, to yield 1,8-disubstituted derivatives, two kinds of equilibrium structures are found, those also stabilized through a one-electron σ bond (X=OH, F, Cl, CN) and those stabilized by the formation of B-X-B bridges (X=H, OMe). These 1,8-BX2 naphthalene derivatives can be considered as analogues of 1,8-NX2 naphthalene proton sponges. While the latter are able to stabilize a proton between the two basic sites, the former are able to stabilize an electron between the two electron-deficient B atoms. Interestingly, when all the H atoms attached to B are substituted by phenyl groups no one-electron σ bonds B-B bonds are formed, due to the dispersion of the unpaired electron in the aromatic substituents.