Thermoelastic diffusion is vital in applications like metallurgy, geophysics, and material testing, especially when moving loads are involved. Moving loads play a crucial role in applications such as high-speed machining, seismic wave propagation, and material stress testing, where understanding interactions between thermal, elastic, and diffusive responses is critical. This paper investigates a two-dimensional thermoelastic-diffusive halfspace under moving thermal and concentration loads using the Moore-Gibson-Thompson (MGT) model. The effects of diffusion, load velocity, and different models on thermophysical quantities are assessed. The governing equations are solved using Laplace-Fourier transforms, and numerical inversion is applied. Graphical representations show that higher load velocities result in lower temperature and concentration magnitudes, while diffusion significantly influences all physical quantities. The study finds that the MGT model provides more stable and physically realistic results compared to classical and generalized models due to its inclusion of thermal and diffusion relaxation times. It also confirms that increased load speed enhances stress intensity but reduces temperature and concentration responses. These findings are relevant to high-speed machining, microelectronics, and transient thermo-diffusive processes.