Difference between Singleton Pattern vs Static Class in Java? Example

Singleton pattern  vs  Static Class (a class, having all static methods) is another interesting questions, which I missed while blogging about Interview questions on Singleton pattern in Java. Since both Singleton pattern and static class provides good accessibility, and they share some similarities e.g. both can be used without creating object and both provide only one instance, at very high level it looks that they both are intended for same task. Because of high level similarities, interviewer normally ask questions like, Why you use Singleton instead of Static Methods, or Can you replace Singleton with static class, and  what are differences between Singleton pattern and static in Java. I