Grippers; you can, and many companies do, make their own compressed air grippers, using a collection of air actuators to provide the gripping motion.
Custom built grippers can work well enough, but their use has penalties. They are usually large and weigh a lot. For large pick and place applications, a large gripper is fine. For smaller, high speed pick and place, you need a gripper built for that use, low in weight and high in speed.
Compressed air equipment manufacturers have risen to the occasion, churning out standard air grippers to suit many applications, grippers that are compact in size, light in weight, lightning fast, and able to handle extraordinary loads when you consider their size.
The gripper has gearing produces movement in the gripper fingers when the piston on the internal cylinder cycles. Air in one in port and the fingers open; air in the other, fingers close.
Gripper fingers are designed for tooling attachment. Tooling might be a simple as rubber nubs or some such, to enable the gripper fingers to better clamp and hold a part.
The strength of the gripper fingers is predicated on how big the piston is inside it, and the available air pressure. Force equals pressure times area, after all, and the force on the internal cylinder piston is transferred to the available gripping force of the gripper fingers.
Grippers do work by opening as well as closing, and putting rubber tips on the outside of the tooling can improve gripping. In this type of use, the gripper fingers are inserted into an opening on a part, and by having the gripper fingers open, that part is effectively gripped.
The types of gripper tooling are unlimited, and predicated on what it is that is to be done by the part that is being gripped.
In the graphic below....