  We show an equivalence between the two categories in the title, thus
establishing a link between Frobenius-linear objects of formal (schematic) and
analytic (adic) nature. We will do this for arbitrary p-complete rings,
arbitrary affine-flat group schemes and without making use of the Frobenius
structure. As a possible application, we take a look at prismatic cohomology of
K3-surfaces and complete intersections of projective space.
