In my opinion a System is actually a gestalt, or a series of gestalts where each object in the system is viewed as a form (figure) on the background of the system as a totality within its boundary. We derive the relations between the things after we specify the things within the systems. The things are what C. Peirce calls Firsts and the relations are what he calls Seconds. The continuity within the background are what he calls Thirds. These are philosophical categories according to Peirce.
Quora answer: Is Whole Systems meaningful as a distinct type of systems thinking?
Systems imply unity and totality. The unity is given by the coherence of the relationships between the things in the system and the totality is everything within the system boundary. But unity and totality are not the same as wholeness. Wholeness is in fact a nondual between unity and totality. Unity and Totality are Kantian categories. Wholeness is synthesis, and synthesis precedes analysis which allows us to distinguish unity from totality as categories.
Systems do not necessarily imply wholeness and so that is an additional characteristic beyond the system schema itself. However, if you look back at the origins of the idea of system it was organisms with wholeness that were the entities that gave rise to the ideal.
Systems since they are composed of firsts, are a lot like Sets, with the boundary being the container of the elements of the set. However, the background of the gestalt is a lot like a mass. So Systems are combinations of set and mass like characteristics. Masses are characterized by boundaries that contain instances. If we look at Mereology it talks about the parts in the whole as individuals but not about the boundary. So to get a whole you need to combine mass with mereology and this is called mereotopology. So to get a whole you needed to add a mereology to Systems.
This is all to say that Whole Systems Theory is different than mere Systems by the addition of Mereology.