c# difference between static member or static constructor and singleton

Is there any difference /tradeoff between using a static member object and the singleton pattern, I often use the code below in C#, but are there any use cases where the Singleton is preferred?

 public class MyStaticObject
    {
        static MyStaticObject _object =new MyStaticObject();

        // OR with static constructor
        //static MyStaticObject _object;
        //static MyStaticObject()
        //{
        //    _object = new MyStaticObject();
        //    // additional static construction logic...
        //    //   ...
        //}
    }

NOTE: this is not the same question as: Difference between static class and singleton pattern?

and other questions which look at static CLASSES. Here my class is not static, just the singleton object. So I have all the benefits of inheritance as listed in the question in the link, but I am not using the singleton pattern for construction.