We present the cross section for $e^{+}e^{-}to hZ$ with arbitrary sets of electron and $Z$ boson polarizations at the full next-to-leading order in various extended Higgs models, such as the Higgs singlet model (HSM), the inert doublet model (IDM) and the two Higgs doublet model (2HDM). We systematically perform complete one-loop calculations to the helicity amplitudes in the on-shell renormalization scheme, and present the full analytic results as well as numerical evaluations. The deviation $Delta R^{hZ}$ in the total cross section from its standard model (SM) prediction is comprehensively analyzed, and the differences among these models are discussed in details. We find that new physics effects appearing in the renormalized $hZZ$ vertex almost govern the behavior of $Delta R^{hZ}$, and it takes a negative value in most cases. The possible size of $Delta R^{hZ}$ reaches several percent under the theoretical and experimental bounds. We also analyze the deviation $Delta R^{hZ}_{XY}$ in the total cross section times decay branching ratios of the discovered Higgs boson by utilizing the $texttt{H-COUP}$ program. It is found that the four types of 2HDMs can be discriminated by analyzing the correlation between $Delta R^{hZ}_{tautau}$ and $Delta R^{hZ}_{bb}$ and those between $Delta R^{hZ}_{tautau}$ and $Delta R^{hZ}_{cc}$. Furthermore, the HSM and the IDM can be discriminated from the 2HDMs by measuring $Delta R^{hZ}_{WW}$. These signatures can be tested by precision measurements at future Higgs factories such as the International Linear Collider.
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