We investigate both the supercooling and the hysteresis phenomena of the phase transitions between the smectic C* and the smectic CA* phases driven by temperature and electric field, respectively. These two phenomena show similar characteristics for the dependence of transmittance on both the cell thickness and the applied field. The mechanisms for large supercooling and large hysteresis in thin cells are shown to correspond to the suppression of the propagation of solitary wave by the surfaces. Furthermore, these two phenomena are shown to be controlled by a moderate ac field applied across the cell. We present a clear evidence for the existence of at least two field induced subphases (called states here) between the antiferroelectric and the ferroelectric phases. These are found to correspond to the field induced three-layered and four-layered structures through a comparison of experimental results on the tilt angle and its simulation as well as by discrete changes in the texture by increasing the electric field. The correspondence between the thermotropic phases and the field induced states is demonstrated through measurements of the supercooling/superheating and of the hysteresis as a function of the cell thickness. The instability in the field induced states depends strongly on the cell thickness, and the various states are not observed in a cell of 1.6 μm thickness.