We perform comparative studies for four types of the two Higgs Doublet Models (2HDMs) under the precision measurements of the Standard Model (SM) Higgs observables at the proposed Higgs factories. We explore the discovery potential based on the hypothetical deviations in the precision data for the 2HDMs up to one-loop level. We find $5sigma$ observability from the $chi^2$ fitting in a significant theory parameter space at future Higgs factories. For the Type-I 2HDM, regions with $cos(beta-alpha)lesssim -0.1$ or $cos(beta-alpha)gtrsim 0.08$ are discoverable at more than $5sigma$ level. For the other three types of 2HDMs, the $5sigma$ region is even bigger: $|cos(beta-alpha)|gtrsim 0.02$ for $tanbetasim 1$. At small and large values of $tanbeta$, the region in $cos(beta-alpha)$ is further tightened. We examine the extent to which the different 2HDM theories may be distinguishable from one to the other at the $95%$ Confidence Level with four benchmark points as case studies. We show that a large part of the parameter space of the other types of 2HDMs can be distinguished from the benchmark points of the target model. The impacts of loop corrections are found to be significant in certain parameter regions.
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