Measurements are presented of inclusive and differential cross sections for Z boson associated production of top quark pairs (t (t) over barZ) and single top quarks (tZq or tWZ). The data were recorded in proton-proton collisions at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb(-1). Events with three or more leptons, electrons or muons, are selected and a multiclass deep neural network is used to separate three event categories, the t (t) over barZ and tWZ processes, the tZq process, and the backgrounds. A profile likelihood approach is used to unfold the differential cross sections, to account for systematic uncertainties, and to determine the correlations between the two signal categories in one global fit. The inclusive cross sections for a dilepton invariant mass between 70 and 110 GeV are measured to be 1.14 +/- 0.07 pb for the sum of t (t) over barZ and tWZ, and 0.81 +/- 0.10 pb for tZq, in good agreement with theoretical predictions.