To stand as still as a statue is to stand absolutely still, a statue being a sculpture, after all. A statue is a specific kind of sculpture, one that clearly represents a person, an animal, or other living creature.
There's no question that the first thing most people think of when they hear the word statue is the Statue of Liberty. The woman's name is Liberty and there she is, a statue. Any sculpture that represents a person (Liberty, George Washington, Gandhi, or the Mad Hatter) is called a statue. In New York's Central Park, there is a much beloved statue of a dog named Balto, a heroic husky from Alaska.