We present color-magnitude diagrams and luminosity functions of stellar populations in the nearby dwarf galaxy Sextans B, based on VI photometry acquired with the Carnegie Observatories spectroscopic multislit and imaging camera CCD prime-focus camera on the Palomar 5 m telescope. Combining previously published Cepheid observations with our new data, we obtain a distance to Sextans B based on the multiwavelength period-luminosity (PL) relations; BVRI data for eight Cepheids having periods ranging from 4 to 30 days were used. This Population I true distance modulus for Sextans B is found to be (m - M)₀ = 25.69 ± 0.27 mag (1.37 ± 0.18 Mpc) with an extinction value of A_V = 0.05 mag. The Cepheid distance is then compared with the Population II distance, determined by applying the tip of the red giant branch (TRGB) method. A discontinuity in the I-band luminosity function is detected at I = 21.60 ± 0.10 mag. Adopting M_I = -4.04 ± 0.02 mag as the absolute magnitude of the TRGB, and taking into account the Galactic extinction value of A_I = 0.02 mag, we obtain a Population II distance modulus of (m - M)₀ = 25.56 ± 0.10 mag (1.29 ± 0.07 Mpc). Additional systematic uncertainties in the TRGB distance scale probably exist at the 5%-10% level. The agreement between the two distances and their uncertainties derived from distinctly independent methods further demonstrates that the accuracy and precision of the TRGB method as an extragalactic distance indicator are comparable to those of the Cepheid PL relation.