There are 3 other game modes available in singleplayer: OutRun, Time Attack, and OutRun2SP. In OutRun2SP, you get access to 15 arcade tracks from the original OutRun 2. In OutRun, you need to drive your girlfriend through various checkpoints to the goal before the timer hits zero. In Time Attack, you just have to beat the highscore of the current track, racing against ghost cars or the clock.
In every mode, you earn OutRun miles, which are the currency of the game and needed to unlock new cars, upgrades, and additional music-stations.