A measurement of the production of vector bottomonium states, ϒ(1S), ϒ(2S), and ϒ(3S), in Pb + Pb and pp collisions at a center-of-mass energy per nucleon pair of 5.02 TeV is presented. The data correspond to integrated luminosities of 1.38 nb-1 of Pb + Pb data collected in 2018, 0.44 nb-1 of Pb + Pb data collected in 2015, and 0.26 fb-1 of pp data collected in 2017 by the ATLAS detector at the Large Hadron Collider. The measurements are performed in the dimuon decay channel for transverse momentum pμμT < 30 GeV, absolute rapidity |yμμ| < 1.5, and Pb + Pb event centrality 0-80%. The production rates of the three bottomonium states in Pb + Pb collisions are compared with those in pp collisions to extract the nuclear modification factors as functions of event centrality, pμμT, and |yμμ|. In addition, the suppression of the excited states relative to the ground state is studied. The results are compared with theoretical model calculations.