Aluminum–magnesium (Al–Mg) alloys, known for their lightweight properties, are extensively utilized and crucial in the advancement of wire and arc additive manufacturing (WAAM) for direct high-quality printing—a focal point in additive manufacturing research. This study employed 1.2 mm ER5356 welding wire as the raw material to fabricate two sets of 30-layer thin-walled structures. These sets were manufactured using two distinct welding modes, speed-twin pulse (STP) and twin pulse (TP). Comparative evaluations of the surface quality, microstructures, and mechanical properties of the two sets of samples indicated that both the STP and TP modes were suitable for the WAAM of Al–Mg alloys. Analyses of grain growth in the melt pools of both sample sets revealed a non-preferential grain orientation, with a mixed arrangement of equiaxed and columnar grains. The STP mode notably achieved a refined surface finish, a reduced grain size, and a slight increase in tensile strength compared to the TP mode. From the comparison of the tensile data at the bottom, middle, and top of the two groups of samples, the additive manufacturing process in the STP mode was more stable.