  Using the leading twist approach (LTA) to nuclear shadowing, we calculate the
ratios of diffractive and usual parton distributions for a heavy nucleus (Pb)
and the proton, $R_{A/p}=(f_{i/A}^{D(3)}/f_{i/A})/(f_{i/p}^{D(3)}/f_{i/p})$,
for coherent and summed (coherent plus quasi-elastic) nuclear deep-inelastic
scattering. We find that $R_{A/p} \approx 0.5-1$ for quarks as well as for the
ratio of the diffractive and total cross sections $[(d\sigma_{\rm
diff}/dM_X^2)/\sigma_{\rm tot}]_{eA}/[(d\sigma_{\rm diff}/dM_X^2)/\sigma_{\rm
tot}]_{ep}$ and $R_{A/p} \approx 0.5-1.3$ for gluons in a broad range of $x$,
including the kinematics of the Electron-Ion Collider, which reaffirms the
difference from the nuclear enhancement of $R_{A/p}$ predicted in the gluon
saturation framework. We demonstrate that the magnitude of $R_{A/p}$ is
controlled by the cross section of the interaction of hadronic fluctuations of
the virtual photon with target nucleons, which explains an enhancement of
$R_{A/p}$ in the color dipole model and its suppression in LTA. We argue that
the black disk limit corresponds to $R_{A/p}=1$ and $R^{\rm coh}_{A/p}=0.86$
for the summed and coherent scattering, respectively. Relying on an intuitive
definition of the saturation scale, we show that the ratio of the saturation
scales of a heavy nucleus and proton $Q_{sA}^2(b)/Q_{sp}^2(b) \approx 1$ at
small impact parameters $b$ due to the strong leading twist nuclear shadowing
and diluteness of the nuclear density.
