Measurement of D+s and D*+s production in B meson decays and from continuum e+e- annihilation at (s)=10.6 GeV

New measurements of D⁺_s and D^*+_s meson production rates from B decays and from qqbar continuum events near the Υ(4S) resonance are presented. Using 20.8 fb^-1 of data on the Υ(4S) resonance and 2.6 fb^-1 off-resonance, we find the inclusive branching fractions B(B-->D⁺_sX)=(10.93+/-0.19+/-0.58+/-2.73)% and B(B-->D^*+_sX)=(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 D⁺_s-->φπ⁺ branching fraction uncertainty. The production cross sections σ(e⁺e^--->D⁺_sX)×B(D⁺_s-->φπ⁺)=7.55+/-0.20+/-0.34 pb and σ(e⁺e^--->D^*+/-_sX)×B(D⁺_s-->φπ⁺)=5.8+/-0.7+/-0.5 pb are measured at center-of-mass energies about 40 MeV below the Υ(4S) mass. The branching fractions ΣB(B-->D^(*)+_sD^(*))=(5.07+/-0.14+/-0.30+/-1.27)% and ΣB(B-->D^*+_sD^(*))=(4.1+/-0.2+/-0.4+/-1.0)% are determined from the D^(*)+_s momentum spectra. The mass difference m(D⁺_s)-m(D⁺)=98.4+/-0.1+/-0.3 MeV/c² is also measured.