  Holographic duality is argued to relate classes of models that have
equivalent unfolded formulation, hence exhibiting different space-time
visualizations for the same theory. This general phenomenon is illustrated by
the $AdS_4$ higher-spin gauge theory shown to be dual to the theory of 3d
conformal currents of all spins interacting with 3d conformal higher-spin
fields of Chern-Simons type. Generally, the resulting 3d boundary conformal
theory is nonlinear, providing an interacting version of the 3d boundary sigma
model conjectured by Klebanov and Polyakov to be dual to the $AdS_4$ HS theory
in the large $N$ limit. Being a gauge theory it escapes the conditions of the
theorem of Maldacena and Zhiboedov, which force a 3d boundary conformal theory
to be free. Two reductions of particular higher-spin gauge theories where
boundary higher-spin gauge fields decouple from the currents and which have
free boundary duals are identified. Higher-spin holographic duality is also
discussed for the cases of $AdS_3/CFT_2$ and duality between higher-spin
theories and nonrelativistic quantum mechanics. In the latter case it is shown
in particular that ($dS$) $AdS$ geometry in the higher-spin setup is dual to
the (inverted) harmonic potential in the quantum-mechanical setup.
