Metro Apps are applications that are specifically written for Windows 8 using all the advantages that Windows 8 has to offer. They can be put on the Windows 8 app store. http://devcomponents.com/blog/?p=1061
WinForms is the old Windows format that was somewhat replaced by WPF. WPF is much more optimized and contains for example vector graphics. WPF provides much better performance when compared to WinForms applications. It provides a much richer UI experience. It uses XAML for development purposes (XML description of your UI). WinForms and WPF give you the existing Windows Look & Feel.
Metro Apps look much more like Windows Phone 7 applications but with much more functionality (but I think in the future both will converge). They are mainly addressed for the tablet market and touch screens (and hybrid devices in the future). Metro apps can be compared to IPad apps but much richer and with the full power of the Windows operation system.
If you want to write standard Windows applications that use a mouse interface and that work like current Windows application I recommend using WPF.
If you want to specifically address the Windows 8 market and create applications that are touch friendly you have to use Metro application
I think you are should read the materials of forum here :