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Each track is a single run from the start line to the finish, through every checkpoint in order. Miss one and the run does not count. Fall off and you restart from the last checkpoint you crossed - the clock keeps going.
Solo is a time trial: you against the clock and nobody else. Every track has three medal times - bronze, silver and then gold, which is a lap driven about as well as the track allows - and your best run is kept as a ghost to chase. So is the fastest lap anyone has set here, and so is anybody else's, straight off the leaderboard. Beat all of them and the world record is yours.
Multiplayer puts everyone in one room on one track, practising whenever they like. When the host starts a race the grid is the last race reversed - whoever was beaten starts ahead of whoever beat them - and the first race of a room is lined up at random. The host can switch qualifying on instead: a ninety-second session before the race, ordinary practice with a clock on it, where your fastest lap sets your place on the grid and pole goes to the quickest. Then the countdown, then the flag. Cars are solid, so bumping is allowed and encouraged, and where you finish moves your rating.