Java Object Declaration Beyond Common Idiom

when a new object is created in Java it follows the idiom:

Object obj = new Object();
where the Object() constructor matches the object type Object.

But what if it doesn't? I understand from the Oracle Docs on creating objects and polymorphism that the constructor must be in that object's class or one of its subclasses. However, suppose we wanted to declare a new stack. My first instinct would be:

Stack s1 = new Stack();
But I assume it's valid to do it this way, too:

Object s2 = new Stack(); // Is there a difference here? What are we really saying about s2? I'm guessing s2 is simply an empty stack, but only has access to the Object class methods? I'm not sure why someone would ever do this, but I want to solidify my understanding of the Java hierarchy. Are there really any circumstances where someone would use a subclass's constructor when creating a new object?