What is the difference between Singleton Design Pattern and Singleton Object In Java?

This was the question that was asked to me recently in an interview. According to me, it is through singleton pattern we can instantiate singleton objects. But, I would like to know whether I am right or not.

You are right, A Singleton Design Pattern is used to instantiate a Singleton Object:

SingleObject class provides a static method to get its static instance to outside world. SingletonPatternDemo, our demo class will use SingleObject class to get a SingleObject object. source

The code would look like this:

public class SingleObject {

    //create an object of SingleObject
    private static SingleObject instance = new SingleObject();

    //make the constructor private so that this class cannot be
    //instantiated
    private SingleObject() {
    }

    //Get the only object available
    public static SingleObject getInstance() {
        return instance;
    }

    public void showMessage() {
        System.out.println("Hello World!");
    }
}

To call the SingleObject class:

public class SingletonPatternDemo {

    public static void main(String[] args) {
        //illegal construct
        //Compile Time Error: The constructor SingleObject() is not visible
        //SingleObject object = new SingleObject();

        //Get the only object available
        SingleObject object = SingleObject.getInstance();

        //show the message
        object.showMessage();
    }
}

So, the Singleton Design Pattern describes how to use a Singleton Object. WikiLink

Please bear in mind that Singletons are, in fact, global variables in disguise. Thus Singletons are considered to be deprecated.