Tyre pressure influences radial as well as tangential tyre stiffnesses. In order to match the different suspension needs (vibration modes and handling effects) on front and rear axle and the different wheel loads, some vehicles need different inflations.
Tyre pressure effect slip angle ,which is required to produced cornering force which counter side thrust acting on the vehicle while turning or cornering as most of the vehicles have front wheel steering so to increase the slip angle pressure in front tyres kept lower then rear tyres.