  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 $5\sigma$ 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 $5\sigma$ level.
For the other three types of 2HDMs, the $5\sigma$ region is even bigger:
$|\cos(\beta-\alpha)|\gtrsim 0.02$ for $\tan\beta\sim 1$. At small and large
values of $\tan\beta$, 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.
