Anguilliform and carangiform fish have a thinner and thicker body along with a smaller and larger undulating wavelength-based kinematics for their propulsion, respectively. The present work is motivated by the fact that both types of fish are observed to adopt each other's kinematics for a short duration on a needs basis. This study explores the effect of such adaptive kinematics via a 2D computational model, focusing on the underlying fluid dynamics and propulsive performance. The effect of the shape is also studied by considering various series of NACA00XX hydrofoil, based on the fineness ratio (length/thickness) of different anguilliform and carangiform fish reported in the literature. Adaptation of carangiform (anguilliform) mode of undulation kinematics by an anguilliform (carangiform)-shaped hydrofoil is found to result in an increase (decrease) in the thrust coefficient along with a decrease (increase) in the quasipropulsive efficiency. Flow characteristics, such as the pressure distribution around the hydrofoil, the strength of the vortices, and the jet behind the hydrofoil, are correlated with the propulsive performance of two naturally observed and six adaptive cases mimicking anguilliform and carangiform fish-inspired shape and swimming. Fineness ratio and undulation wavelength, as compared to the amplitude envelope, has more influence on the propulsive performance and vortex strength in the wake, except for the protovortex, which is more influenced by the amplitude envelope. Finally, a discussion is presented to connect the present 2D CFD results with some of the observed behavior of the anguilliform/carangiform fish in nature. This bioinspired and biomimetics study on naturally observed and adaptive fish-inspired swimming may assist with the need-based efficient design of underwater vehicles.