I'd say that what they share in common are the immanent forms that exist in natural substances. But I think these forms need to have something analogous to a mental existence themselves in order for our minds to be able to access them.
My epistemology couldn't be more different, since I don't think that our minds "access" something in the natural world that contains or automatically produces knowledge. Human concepts don't hide inside of entities.
Rather, our minds are capable of making distinctions based on sense perception. Our visual system allows us to perceive a table as a solid object (not merely as a smear of color), allowing us to view a table as a singular entity. With an exercise of imagination, we have some choice of where to draw those mental lines, since we could just as easily choose an atom in that table as an entity, or for that matter the entire Earth on which that table stands. However, once we have made that choice, we can mentally distinguish that entity from what it is not.
We can also identify properties of that entity, such as a table's rectangular shape, and other details (perhaps not exactly property-like) such as that the table is a creation of human beings. We can create mental categories based on these details by isolating certain characteristics for our purposes, and omitting others, such as defining a table as "a human created raised surface for the purpose of supporting objects", but not caring whether tables have a rectangular, circular, or other-shaped top surface.
Through the use of definitions, we can include and exclude various entities under consideration into our categories, and the concepts we produce using definitions can form a cognitive system of inter-relations. We may associate tables with eating dinner, for instance, and thus form a complex "worldview".
None of this requires some mystical (mental-like?) forms to exist inside of entities. To exist is to exist as
something, and existing as something means having certain properties and not others. Our senses and minds do the rest. Table-ness does not have to exist inside of a table. The table simply has to fit a useful human-created definition.
In any case, I can see how you would think that God has some sort of automatic knowledge. Your epistemology is something I would describe as "mystical", by which I simply mean that it involves knowledge that is not a product of cognition. I prefer rational epistemologies, by which I mean epistemologies that follows a procedure similar to what I've described above.
(I like your signature, BTW. Big Tolkien fan here.
)
Cool.
eudaimonia,
Mark