We investigated the electronic states of the quasi-one-dimensional organic conductors $delta_{P}$-(BPDT-TTF)$_2$ICl$_2$ and $delta_{C}$-(BPDT-TTF)$_2$ICl$_2$, 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 $delta_P$-type salt with an effective half-filled band behaves as a dimer-Mott (DM) insulator and exhibits a nonmagnetic transition at 25 K, whereas the $delta_C$-type salt with a 3/4-filled band shows a charge ordering (CO) transition just above room temperature and becomes nonmagnetic below 20 K. The optical spectra of the $delta_P$-type salt are composed of two characteristic bands due to intra- and interdimer charge transfers, supporting the DM insulating behavior arising from the strong on-site Coulomb interaction. By contrast, in the $delta_C$-type salt, a single band characterizing the formation of CO arising from the off-site Coulomb interactions is observed. Upon lowering the temperature, the shape of the optical spectra in the $delta_C$-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 CO chain. The temperature dependence of the magnetic susceptibility of the $delta_P$-type salt is well described by a 2D spin-1/2 Heisenberg AFM model on an anisotropic square lattice in the dimerized picture, while in the $delta_C$-type salt, it can be explained by a 2D spin-1/2 Heisenberg AFM model on an anisotropic honeycomb lattice formed in the CO state.
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