By default, the route is optimized for travel time, the result is a fast route which prefers routes with longer distances, but lower travel times over routes with shorter distances at higher travel times. This default is represented by options[routingMode]=FAST and tuned to calculate practical routes a real driver would follow.
Set options[routingMode]=SHORT to obtain routes optimized for short distances, i.e. preferring routes with shorter distances, but higher travel times over routes with longer distances at lower travel times.
It is also possible to optimize the route for monetary costs based on distance, working time and toll costs. See the Monetary Costs concept.
Both routing modes FAST and SHORT do not calculate the absolutely fastest and shortest routes, the results are still meaningful and avoid using rural road and travelling through residential areas. For SHORT it may happen to take a shortcut on a small road to reduce the route distance significantly, but the route will still be valid, if possible. That means that the route will usually only be violated if the FAST route is also violated, hence there is no valid route.
Limitations
The routingMode SHORT will not consider truck routes, so the parameter vehicle[truckRoutes] will be ignored and a warning will be returned. For the profiles BICYCLE and PEDESTRIAN fast and short routes are the same, so the parameter options[routingMode] will be ignored and a warning will be returned.
When calculating short routes, it is not recommended to request alternative routes (results=ALTERNATIVE_ROUTES) or to use the options avoid and prefer turns on passenger side (options[avoid], options[preferTurnsOnPassengerSide]). The resulting routes may not be as expected.
Try it in the Short and Fast Routes code sample.