In aquatic pedestrian locomotion the dynamics of terrestrial and aquatic environments are coupled. Here we study terrestrial running and aquatic punting locomotion of the marine-living crab Pachygrapsus marmoratus. We detected both active and passive phases of running and punting through the observation of crab locomotory behaviour in standardized settings and by three-dimensional kinematic analysis of its dynamic gaits using high-speed video cameras. Variations in different stride parameters were studied and compared. The comparison was done based on the dimensionless parameter the Froude number (Fr) to account for the effect of buoyancy and size variability among the crabs. The underwater spring-loaded inverted pendulum (USLIP) model better fitted the dynamics of aquatic punting. USLIP takes account of the damping effect of the aquatic environment, a variable not considered by the spring-loaded inverted pendulum (SLIP) model in reduced gravity. Our results highlight the underlying principles of aquatic terrestrial locomotion by comparing it with terrestrial locomotion. Comparing punting with running, we show and increased stride period, decreased duty cycle and orientation of the carapace more inclined with the horizontal plane, indicating the significance of fluid forces on the dynamics due to the aquatic environment. Moreover, we discovered periodicity in punting locomotion of crabs and two different gaits, namely, long-flight punting and short-flight punting, distinguished by both footfall patterns and kinematic parameters. The generic fundamental model which belongs to all animals performing both terrestrial and aquatic legged locomotion has implications for control strategies, evolution and translation to robotic artefacts.