Undulatory fishes display a wide range of body amplitudes and wavelengths during steady swimming. These kinematics variations can be associated with differences in morphology (e.g. stiff fish bends less) and are considered as fine-tuning to maintain high swimming efficiency. Yet, we still lack a comprehensive theory that brings biomechanics, physiology, kinematics and hydrodynamics together to explain the kinematics diversity. We have recently proposed a method which automatically translates fish movements into mechanical design guidelines that can be used as a resource for future robotics work. Here, we show that the same method can help us perform multi-species comparisons and generate testable biological hypotheses. We analyse the steady swimming kinematics of ten (sub)carangiform swimmers which exhibit vastly different body shapes and flexural stiffness. We discover that, as diverse as these fishes are, one control strategy may unite them all. What separates fishes, however, are the locations where bending moments are applied. Once these locations are factored in, we see that the kinematics diversity collapses into single swimming pattern that is governed by a simple equation.