We consider a detailed account on the construction of the heavy-quark parton distribution functions for charm and bottom, starting from nf=3 light flavors in the fixed-flavor-number (FFN) scheme and by using the standard decoupling relations for heavy quarks in QCD. We also account for two-mass effects. Furthermore, different implementations of the variable-flavor-number (VFN) scheme in deep-inelastic scattering (DIS) are studied, with the particular focus on the resummation of large logarithms in Q2/mh2, the ratio of the virtuality of the exchanged gauge boson Q2 to the heavy-quark mass squared mh2. Little impact of resummation effects is found in the kinematic range of the existing data on the DIS charm-quark production so that they can be described very well within the FFN scheme. Finally, we study the theoretical uncertainties associated to the VFN scheme, which manifest predominantly at small Q2.