What is the difference between a class having private constructor and a sealed class having private constructor?

Question

Is there any difference between A and B?

Class A has private constructor:

class A
{
    private A()
    { }
}

Class B is sealed and has a private constructor:

sealed class B
{
    private B()
    { }
}

Answer 1

Yes A can be inherited by a nested class, while B cannot be inherited at all. This is perfectly legal:

public class A {
  private A() { }

  public class Derived : A { }
}

Note that any code could create a new A.Derived() or inherit from A.Derived (its constructor is public), but no other classes outside the source text of A can inherit directly from A.

A typical use for something like this is a class with enum-like values but which can have custom behavior:

public abstract class A {
  private A() { }

  public abstract void DoSomething();

  private class OneImpl : A { 
    public override void DoSomething() { Console.WriteLine("One"); }
  }

  private class TwoImpl : A { 
    public override void DoSomething() { Console.WriteLine("Two"); }
  }

  public static readonly A One = new OneImpl();
  public static readonly A Two = new TwoImpl();
}

Answer 2

There is one tiny difference you can get, to do with Code Analysis.

Consider this code:

public class Base
{
    public virtual void Function()
    {
    }
}

public class Derived: Base
{
    public static  Derived Create()
    {
        return new Derived();
    }

    private Derived()
    {
        // Code analysis warning: CS2214 "Do not call overridable methods in constructors".
        Function(); 
    }
}

There is a Code Analysis warning for the Derived constructor, because we are accessing a virtual method from it, which is A Bad Thing.

However, if you make Derived sealed, the Code Analysis warning goes away.

So there's a tiny and contrived difference for you. ;)