A systematic treatment of the influence of the optical feedback (OFB) and the ratio of the radiative and the non-radiative recombination lifetime (τ_r/τ_nr) on the relative intensity noise (RIN) and the system dynamics of a semiconductor laser (SL) is presented. We found that the ratio τ_r/τ_nr causes a significant change in the intensity of noise, states, and route to chaos of such a system. Laser transit from a continuous wave (CW) to a periodic oscillation (PO) becomes faster in terms of the OFB strength by increasing the ratio τ_r/τ_nr. The route to chaos was identified in three distinct operating regions, namely, PO, period doubling (PD), and sub-harmonics (SH), which are dependent on the ratio τ_r/τ_nr, and injection current. In the route to chaos regime, the ratio τ_r/τ_nr triggers a slight shift in the frequency with reference to the frequency of the solitary laser. At upmost levels of the current, the highest value of the ratio τ_r/τ_nr stabilizes the laser and stimulates it to operate in CW or PO. In the strong OFB region, when the ratio τ_r/τ_nr increases, the chaotic operation changed to CW or PO operation and RIN is suppressed close to the quantum noise level.