Xbox 360 games will not work on the original Xbox. Games designed for the Xbox 360 require better hardware, and both hardware and software incompatibilities prevent the games from loading on an original Xbox.
On the other hand, many original Xbox games successfully run on an Xbox 360, but not all games are compatible. Since the two devices have different software and hardware, Microsoft developers had to create a compatibility layer to provide this functionality, and they were not able to provide sufficient compatibility for all games. The Xbox One cannot run Xbox or Xbox 360 games, but Microsoft has indicated that popular games for these platforms should eventually be ported.