We report results on the differential and total cross sections for inclusive production of the charmed particles D*+, D*0, D0, D+, Ds, and c in e+e- annihilations at s=10.55 GeV. Widely used quark fragmentation models are discussed and compared with the measured charmed-particle momentum distributions. This comparison, as well as that with measurements at other center-of-mass energies, shows the need to take QCD corrections into account and their importance for a correct interpretation of the model parameters. The observed rate of D0 and D+ production is compared to the expected total charm production cross section. We measure the probability of a charmed meson being produced as a vector meson and the D*+ decay branching fraction into D0+.