  We study the relations between two different approaches to the holographic
Renormalization Group (RG) flow at the dual gravity level: One is the radial
evolution of the classical equation of motion and the other is the flow
equation given by the holographic Wilsonian RG coming from the cut off
independence. Apparently, the two flows look different. We give general proofs
that the two flows are actually equivalent. The role of the momentum continuity
(MC) is essential. We show that MC together with cutoff independence gives the
evolution equation of the boundary values. Equivalence of conductivity flows in
two paradigm has been shown as an explicit example. We also get the connecting
formula of Green functions and AC conductivity at arbitrary slice in terms of
its value at horizon for various geometry backgrounds.
