I'm reading through the POH for the 172RG I'm flying and I'm confused about Vx and the short-field takeoff speed. To me it seems they should be the same, however, Vx is listed as 67 KIAS and the short-field climb out speed is listed as 63 KIAS. Just looking for some clarity.
Vx is a steady state best angle of climb speed, meaning that if you could instantly be at that speed, you would have the best altitude gain per horizontal distance.
That isn't the scenario in a short-field take-off. You're starting from zero KIAS and
accelerating to optimal climb speed. This acceleration is essentially wasted as far as gaining altitude is concerned and the longer you accelerate, the more you eat up the horizontal distance that is available in the takeoff flight path.
If the obstacle is far away, no big deal, since the distance you use to accelerate is only a small percentage of the total distance to the obstacle, and you more than make up for that by having an optimal climb angle. But if the obstacle is close in, the longer ground run has a larger role in determining the horizontal distance to clear the obstacle, and you'd be better off to leave the ground at a non-optimal speed to begin your climb earlier.
Here is a diagram showing your takeoff technique choices:
(One additional factor is that Vx is a clean airspeed; if you depart with some non-zero flap setting, Vx will be slightly slower, even ignoring the issue I just described.)