  We propose that the $X(3915)$ observed in the $J/\psi\,\omega$ channel is the
same state as the $\chi_{c2}(3930)$, and the $X(3960)$, observed in the
$D_s^+D_s^-$ channel, is an $S$-wave $D_s^+ D_s^-$ hadronic molecule. In
addition, the $J^{PC}=0^{++}$ {component in the $B^+\to D^+D^-K^+$} assigned to
the $X(3915)$ in the current {\it Review of Particle Physics} has the same
origin as the $X(3960)$, which has a mass around 3.94~GeV. To check the
proposal, the available data in the $D\bar D$ and $D_s^+ D_s^-$ channels from
both $ B$ decays and $\gamma\gamma$ fusion reaction are analyzed considering
both the $D\bar D$-$D_s\bar D_s$-$D^*\bar D^*$-$D_s^*\bar D_s^*$ coupled
channels with $0^{++}$ and a $2^{++}$ state introduced additionally. It is
found that all the data in different processes can be simultaneously well
reproduced, and the coupled-channel dynamics produce four hidden-charm scalar
molecular states with masses around 3.73, 3.94, 3.99 and 4.23~GeV,
respectively. The results may deepen our understanding of the spectrum of
charmonia as well as of the interactions between charmed hadrons.
