  We consider the loop-induced production of a single Higgs boson from direct
photon-photon scattering at a photon collider. A dedicated analysis of the
total cross section and the relative strength of the effective $h\gamma\gamma$
coupling is carried out within the general Two-Higgs-Doublet Model (2HDM) and
the Minimal Supersymmetric Standard Model (MSSM). We systematically survey
representative regions over the parameter space, in full agreement with
brought-to-date theoretical and phenomenological restrictions, and obtain
production rates up to $10^4$ Higgs boson events per $500 fb^{-1}$ of
integrated luminosity. We identify trademark phenomenological profiles for the
different $\gamma\gamma \to h$ channels and trace them back to the distinctive
dynamical features characterizing each of these models -- most significantly,
the enhancement potential of the Higgs self-interactions in the general 2HDM.
The upshot of our results illustrates the possibilities of
$\gamma\gamma$-physics and emphasizes the relevance of linear colliders for the
Higgs boson research program.
