These 2 systems have many characteristics in common: in fact, in the past, Dave Weagle (Split Pivot) and Trek (ABP) have been involved because Weagle alleged that Trek had copied the system from him. In a way it's true but Trek just made those small changes to get around the patent.
The Assisted Single Pivot, or “imperfect” quadrilateral, by inserting a rear pin concentric to the wheel axis, allowing the positioning of the brake caliper on the seat stays or low ones.
This positioning significantly reduces the effect of braking forces (Anti-Rise), but not to completely exclude them as we understand marketing. Trek's ABP scheme and Split Pivot scheme (also used by BH Bikes as well as DeVinci) work as an assisted Single Pivot, from a pedaling point of view (Anti Squats), but with different (and better) characteristics from a braking point of view.