The current rule for baseball is unique to the sport. If you play another team at any time, it counts against the 56-game limit of games per season. However, if it's played at some time other than during the official season, its result doesn't count in your won-loss record.
Some schools play this type of game during the Fall, despite the fact that it diminishes the number of regular season games they can play. For example, last Fall, UNC played a game against High Point University. If you count the games on this year's UNC regular season schedule, you'll see that it totals only 55.
At the annual convention of the American Baseball Coaches' Association last month, the majority of the coaches voted to allow a small number of games outside of the regular season that would not count against the regular season total. The NCAA Rules Committee will take that vote under advisement and decide if the rule should be changed.