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Detailed analysis of the magnetic properties of the Hubbard model within dynamical mean-field theory is presented. Using a RPA-like decoupling of two-particle propagators, we derive a universal form for susceptibilities, which captures essential aspects of localized and itinerant pictures. This expression is shown to be quantitatively valid whenever long-range coherence of particle-hole excitations can be neglected, as is the case in large parts of the phase diagram where antiferromagnetism is dominant. The applicability of an interpretation in terms of the two archetypical pictures of magnetism is investigated for the Hubbard model on a body-centered-cubic lattice with additional next-nearest-neighbor hopping t'. For large values of the Coulomb interaction, local-moment magnetism is found to be dominant, while for weakly interacting band electrons, itinerant quasiparticle magnetism prevails. In the intermediate regime and for finite t', a reentrant behavior is discovered, where antiferromagnetism only exists in a finite-temperature interval.