From Halopedia, the Halo wiki
Halo was originally intended for the PC and Macintosh, as a sequel to Bungie's popular game Marathon: Infinity. However, with the release of the Xbox, and Microsoft's purchase of Bungie Software, the game was scrapped and ported as a first-person shooter on the Xbox.
In 2003 however, Bungie along with Gearbox Studios shipped a PC version of Halo which became popular with many PC gamers. However, many were disappointed with the netcode, and people complained that the port was poorly designed, causing lag in online play. Halo: Combat Evolved for PC was created to fix these problems, eventually a program called Halo: Custom Edition followed.