Steve or Hal?
yes, it will be different, just like TOD.
VNAV PATH will compute the distance to the first constrained waypoint. The 'idle' descent is backed off from this point, and will calc TOD. The most common use of this is to set a waypoint at 10K, with a speed restriction of 250, this allows the computer to calc backwards and calc TOD with idle descent to that waypoint. This is by far the most efficient use of the coding. TOD idle to 10K. One can see the perils of having the first coded waypoint as the FAF. (see below)
VNAV geometric is used when there are a number of constrained waypoints, the geometric path is computed at the target speed (not 'idle" descent) This reflects all of the waypoints and speed restrictions. An example of this is waypoint at 10K, spd 250, 5000, speed 180, 3000, speed 160 (or whatever the common ATC ALT/SPD are) The geometric path will be set to maintain these altitude and speed restrictions.
VNAV geometric is used to blend RNP and non-RNP traffic, and to maintain airspace speeds other than idle descent.