In a nutshell, polymorphism is bottom-up method calling. Simply put, using your Animal/Mammal/Cat example:

void test()
{
 Cat simon = new Cat();
 Animal creature = simon;  // safe upcasting
 creature.eat(); // polymorph = Cat.eat()
 Dog rover = new Dog();

  // rover safely upcast to Animal reference
 feed(rover);
 feed(simon);
}
void feed(Animal a )
{
  // creature.eat() = Cat.eat()
  // feed(rover)    = Dog.eat()
  // feed(simon)    = Cat.eat()
  a.eat();
}

Here, it's the Animal.eat() which is polymorphic.

Polymorphism: "Calling a Java/virtual method using a reference to a more generalized superclass of a real object invokes the method in the actual object (the more specific subclass) using a bottom-up searching mechanism".

Your Java Tutorial's definition of polymorphism states that function name overloading is the same thing, which is an incorrect statement."

I have to say that Dave is correct, however, I want to focus on overloading here, so I hope to make both points by adding this note!