Interpersonal movement synchrony (IMS) and brain-to-brain coupling play a crucial role in social behavior across species. In humans, IMS is often studied in structured tasks that require specific body movements, while spontaneous, unstructured movements have received less attention. In this study, we investigated both structured and spontaneous motor coordination in mother-child dyads. We recorded upper-body kinematics and dual-EEG from mothers and their preschool children during motor tasks and spontaneous face-to-face interactions. Our findings show that mother-child dyads synchronize their movements and neural activity, particularly in gamma band oscillations. This motor and neural synchrony evolves across task repetitions, with a strong correlation between motor and neural measures. Further, we observed that only motor synchronization was significantly related to the child's motor development stage, as assessed by the Movement Assessment Battery for Children. These results suggest that gamma band brain-to-brain coupling reflects joint motor coordination and mutual adaptation shaped by structured tasks and spontaneous interpersonal interactions.