  Using the same quenched limit as input, we compare the charmonium spectra
predicted by the coupled-channel model and the screened potential model in the
mass region below 4 GeV, in which the contributions from decay channels
involving P-wave (as well as even higher excited) D mesons can be neglected. We
find that the two models have similar global features in describing charmonium
spectrum since they embody the same effect of the vacuum polarization of
dynamical light quark pairs. This agreement is encouraging for using the
screened potential to further describe the mass spectrum of higher charmonium
in the region above 4 GeV. Applying both models will be helpful to clarify the
nature of the newly discovered "X,Y,Z" mesons in B-factories and other
experiments. In particular, we show the S-wave decay coupling effect on
lowering the $\chi_{c1}(2P)$ mass towards the $D\bar {D^*}$ threshold, in
support of the assignment of the X(3872) as a $\chi_{c1}(2P)$-dominated
charmonium state.
