OK, I did some research and I found an great article from UGA that goes into a LOT of details on the different layers in a tree’s skin (Periderm) https://www.warnell.uga.edu/sites/default/files/publications/Tree%20Anatomy%20Components%20of%20Periderm_14-13.pdf
My understanding from it is that the Vascular Cambium produces Phloem which is the material that is flowing (see Flow’em on p.3) and travels through the Secondary Cortex. When the bark “slips”, it seems the Cortex/Phloem is where is separates. So, technically, the Cabium is on the wood (xylem) side according to the diagram below.
I think ultimately what we are trying to do in grafting is to integrate the periderm of the scion/bud into the periderm of the host tree / root stock - primarily focused on the Phloem. Thus, the Cortex through which the Phloem flows and the Cambium that creates it are key as (@Barkslip said). For cleft grafting you align the layers. For bud grafting you place the layers from the bud in the Cortex on top of the Cambium so that is it creates new Ploem/Cortex that can integrate with the Cortex of the bud.