Is there any difference in the function of the circuit if the capacitor has a shorter wire path to the coil or to the points?
TL;DR put it in the distributor housing, next to the points, where there's space for it and it's designed to go.
At the lowish frequencies associated with the main purpose of the capacitor, suppressing an arc at the points, there should not be too much difference between putting it at the points or the coil. However, to minimise the stray inductance in series with the points which the capacitor cannot control, it's best to minimise the loop area enclosed by the change of path between the points closed and points open current path, this is the loop that comprises the stray inductance.
When you look at what it also does for you, suppressing radio interference, it's best to minimise the loop area enclosed by the change of path between the points closed and points open current path, this is the loop that will radiate RF.
Close to the points, generally it mounts on the same screws that hold the points and connects to the same terminal as wire from the points to the coil.
Briggs and Stratton went one better and integrated the capacitor with the terminal and the points contact, but they have since switched to all electronic ignition.