We revisit the production of a single Higgs boson from direct gamma gamma -scattering at a photon collider. We compute the total cross section sigma(gamma gamma to h) (for h=h0, H0, A0), and the strength of the effective g_{h gamma gamma} coupling normalized to the Standard Model (SM), for both the general Two-Higgs-Doublet Model (2HDM) and the Minimal Supersymmetric Standard Model (MSSM). In both cases the predicted production rates for the CP-even (odd) states render up to 10^4 (10^3) events per 500 invfb of integrated luminosity, in full consistency with all the theoretical and phenomenological constraints. Depending on the channel the maximum rates can be larger or smaller than the SM expectations, but in most of the parameter space they should be well measurable. We analyze how these departures depend on the dynamics underlying each of the models, supersymmetric and non-supersymmetric, and highlight the possible distinctive phenomenological signatures. We demonstrate that this process could be extremely helpful to discern non-supersymmetric Higgs bosons from supersymmetric ones. Furthermore, in the MSSM case, we show that gammagamma-physics could decisively help to overcome the serious impasse afflicting Higgs boson physics at the infamous LHC wedge.
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