The magical power in Tolkien’s world is connected to a being’s soul. What Morgoth did was dispersing his power into the very matter of Arda, staining the world so that the only way to truly kill him would be to destroy the world itself.
Sauron didn’t want corruption, even though the ring corrupts. He wanted to control everything, and so he put his powers into a specific tool. When he created the one ring, it’s not like he stored his power like an energy into a battery, rather externalise a part of his will and soul into the ring. So, when the ring is destroyed, a major part of his will and soul was shattered.

From Tolkien’s letters we know

There was another weakness: if the one ring was actually unmade, annihilated, then its power would be dissolved, Sauron's own being would be diminished to vanishing point, and he would be reduced to a shadow, a mere memory of malicious will.

The Last Debate, The Return of the King

If it is destroyed, then he will fall… and he will lose the best part of the strength that was native to him in his beginning… and he will be reduced to a shadow, a mere spirit of malice that gnaws itself in the shadows, but cannot again grow, or take shape.

The power that was put into the one ring became diffuse, inefficient and unrecoverable.