Educate Me About The Wii's Controls

[Yojimbo]

There is something I dont understand with the controls. If I want to play Wii games that need motionsensor I need to use the wiimote. Then there is classic controller and gamecube controller. Can I use the classic controller to play gamecube games? Or use gc controll for classic games? My friend said that I cant use the classic controller for gc games.