Soft Pneumatic-Network (Pneu-Net) Actuators (SPAs) have been used extensively in making soft grippers, due to their simple driving forms and large bending deformation. However, the capabilities of the regular SPAs in complex soft gripping application environments are alone insufficient. This work, thus, proposes a modular soft gripper that combines the functionalities of regular and herringbone actuators. The bending deformation characteristics of the two actuators under pneumatic pressures are verified by finite element (FE) simulations and experiments. The functional characteristics of the two actuators are investigated experimentally through a series of methods including the blocking force test, lifting test, grasping strength test, and suction force test. The experimental results show that the regular actuator has the advantages of greater longitudinal bending deformation and higher blocking force; while, the herringbone actuator has better lifting stability and grasping strength due to its conformal deformations both in longitudinal and transverse directions. In addition, the vacuum experiments demonstrate that the actuators can lift heavy plate-like objects through vacuum suction. Based on the functional behaviors of the two actuators, the proposed modular gripper is loaded onto automatic equipment, and the gripper is tested to hook, grasp, or lift various objects with different shapes, sizes, and weights. In essence, the modular and multi-functional characteristics of the design make it a promising candidate for relatively complex and advanced gripping applications.