Declare-and-throw vs. throw-without-being-declared exceptions

public void methodA() throws AnException {
    //do something
    throw new AnException();
}

public void methodA() {
    //do the same thing
    throw new AnException();
}

public abstract class AbstractBox {
  public abstract void addItem(Item newItem);
  public abstract void removeItem(Item oldItem);
}

public class MyBox extends AbstractBox {
  public void addItem(Item newItem) throws ItemAlreadyPresentException {...}
  public void removeItem(Item oldItem) throws NoSuchItemException {...}
}

public void boxHandler(AbstractBox box) {
  Item item = new Item();
  box.removeItem(item);
}