In our research, we systematically study the polarization-resolved nonlinear dynamics of a Vertical-Cavity Surface-Emitting Laser (VCSEL) under both continuous-wave (CW) optical injection and 3-line gain-switched (GS) optical frequency comb (OFC) injection, applied orthogonally to its parallel polarization. Our results show that the nonlinear dynamics induced by GS-OFC injection are determined by two factors: (1) the frequencies of the nonlinear dynamics of the VCSEL under CW optical injection and (2) the polarization switching curves for both types of optical injection. Both factors are essential in understanding the physics of the OFCs observed at the VCSEL output. We demonstrate OFCs with approximately 50 GHz width.