“Stack and track” is, indeed, a Tom House/NPA term. “Stack” refers to keeping the head and shoulders stacked upright. “Track” refers to the forward movement of the body after the front foot plants.
According to the NPA mechanics model, the front foot plants and the front leg braces stopping the forward movement of the front hip. That results in the back hip rotating around the front hip and, when combined with front side stability and proper timing, leads to to achieve hip and shoulder separation and delayed shoulder rotation. The shoulders should rotate around an upright spine which means the head and shoulders are stacked upright. While all of this is happening, the body continues to track forward a bit. Thus, delayed shoulder rotation contributes to moving the release point closer to home plate. The final piece is deals with glove arm stability.
There is a “stack and track” version of the towel drill. It simply starts in a position where the stride has taken place and the shoulders have rotated.