To clarify your 2nd question, college football is administrated by the NCAA but the college football playoff system is NOT operated by the NCAA. There is no official NCAA champion, and so sometimes people like to point out that they are two completely separate entities and so any champion is not techincally approved by the NCAA.
An undefeated team could have played a bunch of teams which weren’t all that great, so they could lose to a team that currently has 0 wins because they lost to teams better than the undefeated team.
An informal championship would either be in a tournament not run by the sport’s agencies or it is official games but not a tournament event, so the champion is found via stats.
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