You're putting two things together. The NFL had a game with last season's champion vs. College All-Stars that was the first pre-season game before the HOF Game was. I remember the Jets playing in it the summer after Super Bowl III. It was invented in the 30's by Arch Ward, the Chicago sports editor who also thought up the MLB All-Star Game. In the 30's a game between College All-Stars and an NFL team was apparently competitive. It was eventually dropped because it was an awful game by the 60's and the NFL hated letting blue chip draft choices stay out of training camps to get ready for it.
The AFL started with an East vs. West All-Star game but tried a champions vs. the rest of the league format for one year, 1965 (= why the Bills played it). That was a post-season game like it is now. The source for the format was the old 6-team NHL, which did the same thing but, IIRC, played the game mid-season. I don't remember what the AFL did in '66 but since the champion had an extra game (SB I) I think they went back to East vs. West.
God I feel old knowing this stuff.