Like all echinoids, a sand dollar has an internal skeleton of fused calcite plates called a test, worn beneath a living skin. In life the test is hidden under thousands of tiny spines, tube feet and cilia that beat continuously to move food particles toward the mouth. The animal is not smooth and not white.
After death the soft tissue decays, the spines detach, and sun and seawater bleach the remaining test. The five-petalled pattern visible on the top is the petaloid, a set of pores where specialised respiratory tube feet passed through the plates.
A second common belief is that the small pale fragments inside a rattling test are teeth, or that they are seeds or doves. They are the elements of the animal's Aristotle's lantern, the jaw apparatus, which fall loose once the surrounding tissue is gone. Collecting a living sand dollar is often restricted for exactly this reason, since it is easy to mistake a live animal for an empty shell.