Obviously the Xbox 360 has a left and right trigger and a left and right bumper, while the original Xbox has a left and right trigger and a white button and a black button.

However, this doesn't mean you can use Xbox console cheats when playing Xbox games on your Xbox 360!

In fact, the cheats are exactly the same. You just need to replace the black button with the right bumper and replace the white button with the left bumper.

Black button --> right bumper (RB)
White button --> left bumper (LB)

Enjoy!