What is difference between using singleton class and class with static methods?

Question

what is need of singleton(state is fixed ) class if I have class with static methods (fixed behaviors )?

Answer 1

With the singleton it is easier to replace the instance if needed, for example, for testing.

Answer 2

I think one of the best arguments for using a singleton rather than a class with purely static methods is that it makes it easier to introduce multiple instances if this turns out to be required later. It is not uncommon to see applications where there is no fundamental reason to restrict a class to a single instance, but the authors did not envision any extension of their code, and found it easier to use static methods. Then when you want to extend the application later it is much harder to do so.

Being able to replace the instance for testing (or other reasons) is also a good point, and being able to implement an interface also helps with this.