This file has the original Bad C# CommandExecutor, a good one, and a good one using the same names as you used for the VB version. Original tests are at bottom, with extra set for the VBish CommandExecutor

CommandExecutor

using NUnit.Framework;
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace ChrissieGist5012518
{
    public class BadCommandExecuter : ICommandExecuter
    {
        public void Execute<TCommand>() where TCommand : class, ICommand, new()
        {
            var command = new TCommand();
            command.Execute();
        }

        //same terms as the C# version
        public void Execute<TCommandWithParameter, TParameterType>(TParameterType parameter)
            where TCommandWithParameter : class, ICommandWithParameter<object>, new()       // <-- that object should be TParameterType
        {
            var command = new TCommandWithParameter();
            command.ExecuteWitParameter(parameter);
        }

    }

    public class CommandExecuter : ICommandExecuter
    {
        public void Execute<TCommand>() where TCommand : class, ICommand, new()
        {
            var command = new TCommand();
            command.Execute();
        }

        //same terms as the C# version
        public void Execute<TCommandWithParameter, TParameterType>(TParameterType parameter)
            where TCommandWithParameter : class, ICommandWithParameter<TParameterType>, new()
        {
            var command = new TCommandWithParameter();
            command.ExecuteWitParameter(parameter);
        }

    }

    // used parameter names for the generics that matched your VB code
    public class CommandExecuterVBish : ICommandExecuter
    {
        public void Execute<TCommand>() where TCommand : class, ICommand, new()
        {
            var command = new TCommand();
            command.Execute();
        }

        // same terms as the VB version
        public void Execute<TCommand, TParameter>(TParameter parameter)
            where TCommand : ICommandWithParameter<TParameter>, new()
        {
            var command = new TCommand();
            command.ExecuteWitParameter(parameter);
        }

    }

    #region Interfaces

    public interface ICommandExecuter
    {

    }

    public interface ICommand
    {
        void Execute();
    }

    public interface ICommandWithParameter
    {
        void Execute();
    }

    public interface ICommandWithParameter<T>
    {
        void ExecuteWitParameter(T Parameter);
    }

    #endregion

    [TestFixture]
    public class BadTests
    {
        [Test]
        public void IfExecuteExecutesCommandWithParameter()
        {
            var executer = new BadCommandExecuter();
            Assert.Throws<System.NotImplementedException>(() => executer.Execute<TestCommandWithParameter, String>("test"));
        }


        private class TestCommandWithParameter : ICommandWithParameter<object>
        {
            public void ExecuteWitParameter(object parameter)
            {
                throw new System.NotImplementedException();
            }
        }

    }

    [TestFixture]
    public class WhatIWantTests
    {
        [Test]
        public void IfExecuteExecutesCommandWithParameter_VBStyleParamNames()
        {
            var executer = new CommandExecuterVBish();
            Assert.Throws<System.NotImplementedException>(() => executer.Execute<TestCommandWithParameter, string>("test"));
        }

        [Test]
        public void IfExecuteExecutesCommandWithParameter()
        {
            var executer = new CommandExecuter();
            Assert.Throws<System.NotImplementedException>(() => executer.Execute<TestCommandWithParameter, string>("test"));
        }

        private class TestCommandWithParameter : ICommandWithParameter<string>
        {
            public void ExecuteWitParameter(string parameter)
            {
                throw new System.NotImplementedException();
            }
        }
    }

}