Formula One 06 is the fifteenth game of the official Formula One video games series and the final one released on PS2. The game continues the tradition of a career mode, an option in place since the 2004 game. Formula One 06 uses the previous F1 game engine but with minor modifications (team and driver select with team mode has a team logo).
Source: Wikipedia, "Formula One 06", available under the CC-BY-SA License.
Formula One Championship Edition is the updated version of the game released for the PS3 in 2007. The game covers the 2006 F1 season and features updated visuals for the PS3 including a lot more detail, Sixaxis compatibility, real time reflections and shadows, car reflections on wet circuits and new "dynamic" wet weather effects.
Source: Wikipedia, "https://en.wikipedia.org/wiki/Formula_One_Championship_Edition", available under the CC-BY-SA License.