New measurements of Ds+ and Ds*+ meson prodn. rates from B decays and from q-q continuum events near the U(4S) resonance are presented. Using 20.8 fb-1 of data on the U(4S) resonance and 2.6 fb-1 off-resonance, we find the inclusive branching fractions B(B -> Ds+X)=(10.93+-0.19+-0.58+-2.73)% and B(B -> Ds*+X)=(7.9+-0.8+-0.7+-2.0)%, where the first error is statistical, the second is systematic, and the third is due to the Ds+ -> jp+ branching fraction uncertainty. The prodn. cross sections s(e+e- -> Ds+X)*B(Ds+ -> jp+)=7.55+-0.20+-0.34 pb and s(e+e- -> Ds*+-X)*B(Ds+ -> jp+)=5.8+-0.7+-0.5 pb are measured at center-of-mass energies about 40 MeV below the U(4S) mass. The branching fractions SB(B -> Ds(*)+D(*))=(5.07+-0.14+-0.30+-1.27)% and SB(B -> Ds*+D(*))=(4.1+-0.2+-0.4+-1.0)% are detd. from the Ds(*)+ momentum spectra. The mass difference m(Ds+)-m(D+)=98.4+-0.1+-0.3 MeV/c2 is also measured. [on SciFinder (R)]