In this paper, we present Salamandra robotica II: an amphibious salamander robot that is able to walk and swim. The robot has four legs and an actuated spine that allow it to perform anguilliform swimming in water and walking on the ground. The paper first presents the new robot hardware design, which is an improved version of Salamandra robotica I. We then address several questions related to body-limb coordination in robots and animals that have a sprawling posture like salamanders and lizards, as opposed to the erect posture of mammals (e.g., in cats and dogs). In particular, we investigate how the speed of locomotion and curvature of turning motions depend on various gait parameters such as the body-limb coordination, the type of body undulation (offset, amplitude, and phase lag of body oscillations), and the frequency. Comparisons with animal data are presented, and our results show striking similarities with the gaits observed with real salamanders, in particular concerning the timing of the body's and limbs' movements and the relative speed of locomotion.