Here's a breakdown:

* ATP synthase is a complex enzyme that catalyzes the synthesis of ATP from ADP and inorganic phosphate (Pi). This process is driven by the proton gradient across the mitochondrial membrane (in eukaryotes) or the cell membrane (in prokaryotes).

* ADP (adenosine diphosphate) is the "de-energized" form of ATP.

* ATP (adenosine triphosphate) is the "energized" form, carrying a high-energy phosphate bond that can be broken to release energy for cellular processes.

While ATP synthase is the main player, other enzymes like kinases and phosphatases can also participate in the ATP-ADP cycle, depending on the specific biochemical reactions.