Every finisher in a big American road race receives two times that differ, sometimes substantially. Both are correct, and they answer different questions.
Gun time measures the race
Gun time runs from the starting signal to the finish, identically for everyone. It is the time used to determine finishing places and prize positions.
Placing has to use a common start because a race is a contest between runners. Someone who started later cannot be credited with a better position for having crossed the line later.
This is why elite fields are started at the front. Their gun time and their actual running time are effectively the same.
Chip time measures the runner
Chip time runs from the moment a runner crosses the start mat to the moment the finish mat is crossed, capturing only that individual's time on course.
In a field of tens of thousands, reaching the start line can take many minutes. Chip time removes that delay, which is the number the runner cares about.
Qualifying standards for major marathons generally accept chip time, since the question there is what the runner ran rather than where they placed.
How the mats actually work
Timing mats detect a transponder carried by the runner, usually attached to the bib, and log the crossing with a timestamp against the runner's identifier.
Intermediate mats along the course produce split times and also serve as a check that the full route was run.
Missed reads happen, which is why races place multiple mats at key points and reconstruct missing splits from the surrounding data.
The course-cutting problem
Intermediate mats exist substantially to detect runners who did not complete the course. A finish time without the expected splits triggers a review.
Race organizers act on this data routinely, disqualifying finishers whose split pattern is inconsistent with the route.
The detection is only as dense as the mats. Races add checkpoints where shortcuts are geographically plausible rather than at even intervals.
Why both times are published
Publishing only gun time would misrepresent most participants' performance. Publishing only chip time would make the results meaningless as a competition.
Results systems therefore carry both, with placing computed on gun time and personal comparison invited on chip time.
Confusion persists because the two are printed adjacently without explanation, and a runner seeing two different times naturally assumes one is wrong.

