What are the differences between `async void` (with no await) vs `void`

Taken from article on async await by Stephen Cleary:

Figure 2 Exceptions from an Async Void Method Can’t Be Caught with Catch

private async void ThrowExceptionAsync()
{
  throw new InvalidOperationException();
}
public void AsyncVoidExceptions_CannotBeCaughtByCatch()
{
  try
  {
    ThrowExceptionAsync();
  }
  catch (Exception)
  {
    // The exception is never caught here!
    throw;
  }
}

... any exceptions thrown out of an async void method will be raised directly on the SynchronizationContext that was active when the async void method started...

What does that actually mean? I wrote an extended example to try and glean more info. It has the same behaviour as Figure 2:

static void Main()
{

    AppDomain.CurrentDomain.UnhandledException += (sender, ex) => 
    {
        LogCurrentSynchronizationContext("AppDomain.CurrentDomain.UnhandledException");
        LogException("AppDomain.CurrentDomain.UnhandledException", ex.ExceptionObject as Exception);
    };

    try
    {
        try
        {
            void ThrowExceptionVoid() => throw new Exception("ThrowExceptionVoid");

            ThrowExceptionVoid();
        }
        catch (Exception ex)
        {
            LogException("AsyncMain - Catch - ThrowExceptionVoid", ex);
        }

        try
        {
            // CS1998 C# This async method lacks 'await' operators and will run synchronously. 
            async void ThrowExceptionAsyncVoid() => throw new Exception("ThrowExceptionAsyncVoid");

            ThrowExceptionAsyncVoid();
        }
        // exception cannot be caught, despite the code running synchronously.
        catch (Exception ex) 
        {
            LogException("AsyncMain - Catch - ThrowExceptionAsyncVoid", ex);
        }
    }
    catch (Exception ex)
    {
        LogException("Main", ex);
    }

    Console.ReadKey();
}

private static void LogCurrentSynchronizationContext(string prefix)
    => Debug.WriteLine($"{prefix} - " +
        $"CurrentSynchronizationContext: {SynchronizationContext.Current?.GetType().Name} " +
        $"- {SynchronizationContext.Current?.GetHashCode()}");

private static void LogException(string prefix, Exception ex)
    => Debug.WriteLine($"{prefix} - Exception - {ex.Message}");

Debug output:

Exception thrown: 'System.Exception' in ConsoleApp3.dll
AsyncMain - Catch - ThrowExceptionVoid - Exception - ThrowExceptionVoid
Exception thrown: 'System.Exception' in ConsoleApp3.dll
An exception of type 'System.Exception' occurred in ConsoleApp3.dll but was not handled in user code
ThrowExceptionAsyncVoid
AppDomain.CurrentDomain.UnhandledException - CurrentSynchronizationContext:  - 
AppDomain.CurrentDomain.UnhandledException - Exception - ThrowExceptionAsyncVoid
The thread 0x1c70 has exited with code 0 (0x0).
An unhandled exception of type 'System.Exception' occurred in System.Private.CoreLib.ni.dll
ThrowExceptionAsyncVoid
The program '[18584] dotnet.exe' has exited with code 0 (0x0).

I want more details

• If there is no current synchronization context (as in my example), where is the exception raised?
• What are the differences between async void (with no await) and void
  • The compiler warns CS1998 C# This async method lacks 'await' operators and will run synchronously.
  • If it runs synchronously with no await, why is it behaving differently from simply void?
  • Does async Task with no await also behave differently from Task?
• What are the differences in compiler behaviour between async void and async Task. Is a Task object really created under-the-hood for async void as suggested here?

Edit. To be clear, this isn't a question about best practices - it is a question about compiler / runtime implementation.