Come on, even WPF runs under browser why SilverLight ?
Yes there is something called as WPF browser application which can run WPF in browser. For WPF browser application you need .Net framework to be installed in the client location while for silver light you need only the plug-in. So in other words WPF browser applications are OS dependent while SilverLight is not. SilverLight plug-in can run in other OS other than windows while we all know .NET framework only runs in windows.