What's the difference between
this.Loaded += new RoutedEventHandler(MainWindow_Loaded);
and
childWindow.MyEvent += new EventHandler(childWindow_MyEvent);
I assume you want to know what is the difference between events and routed events. These 2 articles can help you:
https://msdn.microsoft.com/en-us/library/ms742806(v=vs.100).aspx (MSDN article)
http://joshsmithonwpf.wordpress.com/2008/03/18/understanding-routed-commands/ (excellent article on routed commands, which also contains a very good explanation of routed events)
In short, RoutedEvents are routed. They can bubble or expand the visual tree until they hit the handler.
Standard events are just a direct subscription.