The Genesis game was College Football USA '96. The '97 version also had playoffs, but it wasn't as good a game overall.
Even though it had a new name, the game was made by the same team that did Bill Walsh College Football (High Score Productions).
Bill Walsh '95 also had the option to go to a playoff system or to bowl games.
I didn't play the '98 version, but I know NCAA '99 let you have a 16-team playoff at the end of the season if you wanted to. They kept the playoff option in the game until the final PS1 version (NCAA 2001).
Once the series went to PS2, the playoff feature never came back.