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Abstract 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 $$ {R}_{A/p}=\left({f}_{i/A}^{D(3)}/{f}_{i/A}\right)/\left({f}_{i/p}^{D(3)}/{f}_{i/p}\right) $$ , for coherent and summed (coherent plus quasi-elastic) nuclear deep-inelastic scattering. We find that R A/p ≈ 0.5 − 1 for quarks as well as for the ratio of the diffractive and total cross sections dσ diff / dM X 2 / σ tot eA / dσ diff / dM X 2 / σ tot ep $$ {\left[\left({d\sigma}_{\textrm{diff}}/{d M}_X^2\right)/{\sigma}_{\textrm{tot}}\right]}_{eA}/{\left[\left({d\sigma}_{\textrm{diff}}/{d M}_X^2\right)/{\sigma}_{\textrm{tot}}\right]}_{ep} $$ and R A/p ≈ 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 A / p coh $$ {R}_{A/p}^{\textrm{coh}} $$ = 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 ≈ 1 $$ {Q}_{sA}^2(b)/{Q}_{sp}^2(b)\approx 1 $$ at small impact parameters b due to the strong leading twist nuclear shadowing and diluteness of the nuclear density.