We model the situation of two lasers in a face-to-face arrangement, optically coupled through an attenuating element, where the distance between the lasers is on a scale typical in photonic integration (hundreds of micrometers to millimeters). We account for the existence of a frequency difference between the two single-mode lasers. Modified versions of the Lang-Kobayashi equations were employed to describe the interaction. By solving this delay differential equation system, we characterized different dynamical regimes including one- and two-color states and self-pulsations. We focus on the effect varying coupling strength and detuning between the lasers has on the frequencies of the lasers. Using the results of this frequency study, we identify the bifurcations causing changes between the different frequency regimes.