Grid-forming (GFM) inverters, like synchronous generators (SGs), form voltage at their terminals and are considered crucial for enabling high renewable energy integration. Most GFM controllers mimic the power-synchronization characteristics of the SG rotor's swing dynamics to synchronize with the system. However, GFM inverters differ significantly from SGs in both design and control. This paper systematically explores these differences. The analysis reveals that the coupling between steady-state and transient performance in traditional GFM controllers, both influenced by the active power-frequency droop gain, along with the absence of features like large stator inductance, damper windings, and power system stabilizers (PSS), may result in SGs having superior disturbance rejection in the small-signal domain. Building on these insights, a novel GFM control technique with improved disturbance rejection performance is proposed. A comparative stability analysis is performed to evaluate the robustness of the proposed technique against conventional GFM controls under various grid conditions. The effectiveness of the proposed control method is further validated through MATLAB/Simulink simulations and real-time hardware-in-the-loop testing in diverse power system scenarios.