`throw` vs. `throw ex` in C#

README.md

throw ex gives the following stack trace. Notice that THIS_METHOD_THROWS() is missing.

System.InvalidOperationException: Operation is not valid due to the current state of the object.
   at ConsoleApplication1.Program.CatchThrowEx() in C:\Code\ConsoleApplication1\ConsoleApplication1\Program.cs:line 54
   at ConsoleApplication1.Program.Main() in C:\Code\ConsoleApplication1\ConsoleApplication1\Program.cs:line 12

throw gives the following stack trace, which helpfully includes THIS_METHOD_THROWS() where the exception originated.

System.InvalidOperationException: Operation is not valid due to the current state of the object.
   at ConsoleApplication1.Program.THIS_METHOD_THROWS() in C:\Code\ConsoleApplication1\ConsoleApplication1\Program.cs:line 60
   at ConsoleApplication1.Program.CatchThrow() in C:\Code\ConsoleApplication1\ConsoleApplication1\Program.cs:line 42
   at ConsoleApplication1.Program.Main() in C:\Code\ConsoleApplication1\ConsoleApplication1\Program.cs:line 24

CSharp_Throw_vs_ThrowEx.cs

using System;

namespace ConsoleApplication1
{
    public class Program
    {
        public static void Main()
        {
            try
            {
                Console.WriteLine("THROW EX:");
                CatchThrowEx();
            }
            catch (Exception ex)
            {
                Console.WriteLine(ex);
            }

            Console.WriteLine();

            try
            {
                Console.WriteLine("THROW:");
                CatchThrow();
            }
            catch (Exception ex)
            {
                Console.WriteLine(ex);
            }

            Console.ReadKey();
        }

        static void CatchThrowEx()
        {
            try
            {
                THIS_METHOD_THROWS();
            }
            catch (Exception ex)
            {
                throw ex;
            }
        }

        static void CatchThrow()
        {
            try
            {
                THIS_METHOD_THROWS();
            }
            catch (Exception)
            {
                throw;
            }
        }

        static void THIS_METHOD_THROWS()
        {
            throw new InvalidOperationException();
        }
    }
}