This work presents a comparison of radiative magnetohydrodynamics (MHD) Bingham and Newtonian fluids across a nonlinear stretching sheet (SS), considering thermoelectric effects, chemical processes, and Joule heating. The governing equations are converted into Ordinary Differential Equation (ODE) form using suitable non-dimensional variables and parameters as well as employed a numerical strategy that combines the Nachtsheim-Swigert (N-S) shot method with the 6th order Runge-Kutta (R-K) algorithm. Comparing the behaviors of Bingham and Newtonian fluids is the main objective, which reveals intricate linkages between different physical phenomena, chemical processes, and radiative MHD on nonlinear stretching sheets. The dynamics of concentration, primary and secondary velocities, skin friction, heat and mass transfer rates, temperature, and other dimensionless parameters are graphically presented in the research. Important results indicate that compared to Newtonian fluid flow, Bingham fluid flow decreases primary velocity by 7.01% greater. Furthermore, on a nonlinear stretching sheet, temperature increases by 38.09% higher than on a linear one. In Newtonian fluid, thermal radiation acts as an increasing factor but in Bingham fluid, it acts as a decreasing factor. At a 95% confidence level, the regression analysis shows a substantial interaction between factors influencing the Nusselt number, with correlation values (R2) of 98.11% for Bingham fluids and 98.79% for Newtonian fluids. The Nusselt number and Joule heating for Newtonian fluid have a correlation study of 90.90%, whereas for Bingham fluid it is 83.69%. The improved thermal performance linked with Bingham fluid flow is highlighted by these studies, which have potential in tissue engineering, medication delivery systems, and renewable energy.