Using shift p/s means you retire from the race (and gets you a nice 10 point penalty if it's done outside of a pit garage), and there is of course no reset. If you timeout you can rejoin, though if you've just raped your engine or were stuck in the gravel and timed out on purpose you can expect a big penalty.
The tracker simply counts up all the complete laps from each team and sorts the teams by laps, time they crossed the line and then whoever is first with their lap packet in the database.