We investigated the electronic states of the quasi-one-dimensional organic salts δP′-(BPDT-TTF)2ICl2 and δC′-(BPDT-TTF)2ICl2, both of which are insulating at room temperature owing to strong electron correlations. Through measurements of electrical resistivity, optical conductivity, and magnetic susceptibility, as well as band-structure calculations, we have revealed that the two materials possess completely different ground states, even though they have the same chemical composition and stacking configuration of the donor molecules. We have found that the δP′-type salt with an effective half-filled band behaves as a dimer-Mott insulator and exhibits a phase transition to a nonmagnetic state at 25 K, whereas the δC′-type salt with a 3/4-filled band shows a charge ordering transition just above room temperature and becomes nonmagnetic below 20 K. The optical spectra of the δP′-type salt are composed of two characteristic bands due to intra- and interdimer charge transfers, supporting the dimer-Mott insulating behavior arising from the strong on-site Coulomb interaction. By contrast, in the δC′-type salt, a single band characterizing the formation of charge ordering arising from the off-site Coulomb interactions is observed. Upon lowering the temperature, the shape of the optical spectra in the δC′-type salt becomes asymmetric and shifts to much lower frequencies, suggesting the emergence of domain-wall excitations with fractional charges expected in a one-dimensional charge-ordered chain. The temperature dependence of the magnetic susceptibility of the δP′-type salt is well described by a two-dimensional (2D) spin-1/2 Heisenberg antiferromagnetic model on an anisotropic square lattice in the dimerized picture, while in the δC′-type salt, it can be explained by a 2D spin-1/2 Heisenberg antiferromagnetic model on an anisotropic honeycomb lattice formed in the charge-ordered state. These completely different ground states between the δP′- and δC′-type salts come from the difference of degree of dimerization of two face-to-face BPDT-TTF molecules.