There are two types of wave that will be generated when a stone is dropped into a body of water.
A gravity wave is formed when the falling stone strikes the water surface and pushes aside the water that is directly in its way. This water then piles up in a ring around the stone as it tries to move sideways, and then that "pileup" propagates away. Gravity furnishes the restoring force that strives to pull back down that raised ring of water. These waves are large and fast-moving, and are created by stones bigger than ~ a millimeter or two in diameter that strike the water at speed.
A capillary wave is formed when the stone deforms the surface layer of the water during its entry, which acts like a stretched and elastic membrane that pushes back against the falling stone. Surface tension furnishes the restoring force which strives to flatten back out the surface of the water. These waves are very small and slow moving, and are formed by stones less than ~ a millimeter or two in diameter that strike the water gently.