Adrian is right, although to tell the truth, they often CAN be used interchangeably. "Shiver" is usually a continuous action, but sometimes you may read something like "a shiver went through him," which is the same as a quiver -- a brief moment of shaking slightly. And even though "shiver" is the word most commonly associated with cold, you may also sometimes read about someone "quivering" from the cold.
I would say that in literary language, they're more often interchangeable. In everyday conversation, "shivering" is continuous, and a "quiver" is brief.