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Charged-hadron distributions in heavy-flavor jets are measured in proton-proton collisions at a center-of-mass energy of TeV collected by the LHCb experiment. Distributions of the longitudinal momentum fraction, transverse momentum, and radial profile of charged hadrons are measured separately in beauty and charm jets. The distributions are compared to those previously measured by the LHCb collaboration in jets produced back-to-back with a Z boson, which in the forward region are primarily light-quark-initiated, to compare the hadronization mechanisms of heavy and light quarks. The observed differences between the heavy- and light-jet distributions are consistent with the heavy-quark dynamics expected to arise from the dead-cone effect, as well as with a hard fragmentation of the heavy-flavor hadron as previously measured in single-hadron fragmentation functions. This measurement provides additional constraints for the extraction of collinear and transverse-momentum-dependent heavy-flavor fragmentation functions and offers another approach to probing the mechanisms that govern heavy-flavor hadronization.