Fin Ray soft grippers, as a notable passive compliant structures, can be easily actuated by external devices to adapt their shape to conform to a grasped object. Their unique ability is aided by their V-shaped structure and morphable material utilized by the Fin Ray finger. Thus, when the internal structure changes, the adaptability and grasping abilities also change. However, related works focus on the effects of changing key parameters on the grasping performance based on the Festo structure, and few works have explored the effects of changing the internal structure. To close the research gap, four different Fin Ray structures are presented in this article, and a parameter determination process was carried out by maximizing their adaptability by investigating the key parameters of each structure through finite element analysis. Then, the force responses of four selected Fin Ray structures are analyzed and experimentally validated. The results show that the No Internal Filling structure obtained by omitting the crossbeams is ideal for grasping delicate targets with the best adaptability and the minimum resultant force. The cross structure attained by adding vertical beams connected to crossbeams decreases the adaptability of the Fin Ray finger but significantly increases the contact force. The unsymmetric design of the branched structure significantly enhances the final contact force while improving the passive adaptation to objects. Thus, the application of the Fin Ray finger ranges from adaptive delicate grasping tasks to high-force manipulation tasks.