Twinning is a prominent deformation mode that accommodates plasticity in many materials. This study elucidates the role of deformation rate on the atomic-scale mechanisms that govern twin boundary migration. Examination of Mg single crystals deformed under quasi-static compression was compared with crystals deformed via plate impact. Evidence of two mechanisms was uncovered. Atomic-level observations using high-resolution transmission electron microscopy revealed that twin boundaries in the <a>-axis quasi-statically compressed single crystals are relatively smooth. At these modest stresses and rates, the twin boundaries were found to migrate predominantly via shear (i.e., disconnection nucleation and propagation). By contrast, in the plate-impacted crystals, which are subjected to higher stresses and rates, twin boundary migration was facilitated by local atomic shuffling and rearrangement, resulting in rumpled twin boundaries. This rate dependency also leads to marked variations in twin variant, size, and number density in Mg. Analogous effects are anticipated in other hexagonal closed-packed crystals.