This study investigates the nonlinear dynamics of Brushless DC (BLDC) motors using the MATLAB/Simulink platform, emphasizing system identification through the Least Squares (LS) method and Nonlinear Autoregressive Network With Exogenous Inputs (NARX) models with variable regressors. Accurate data-driven models derived from these techniques are essential for designing efficient feedback control systems, enabling precise motor dynamics representation and facilitating early fault detection by identifying deviations from normal operation. A detailed simulation of the BLDC motor under no-load conditions is performed to analyze the speed response and ripple effects in torque and speed, underscoring the need for effective modeling and control. Comprehensive datasets are generated to develop LS and NARX models across varying operational conditions. A variable step input voltage signal with both ascending and descending steps is employed for training, while a distinct validation signal of similar trends but different magnitudes is used for performance evaluation. All techniques are benchmarked using identical training and validation signals. Among the models, the NARX model with customized regressors demonstrated superior performance, achieving 99.1% training accuracy and 98.01% validation accuracy in predicting motor dynamics. All the models are further tested under real-time signal conditions like ramp-up acceleration, deceleration, & turning and noisy signal conditions to evaluate the robustness and accuracy of these models in real-world conditions. The findings highlight the NARX model's potential to enhance control strategies and improve BLDC motor stability, with statistical analysis confirming the robustness and effectiveness of the proposed approach.