We study quantum frequency translation and two-color photon interference enabled by the Bragg scattering four-wave mixing process in optical fiber. Using realistic model parameters, we computationally and analytically determine the Green function and Schmidt modes for cases with various pump-pulse lengths. These cases can be categorized as either "non-discriminatory" or "discriminatory" in regards to their propensity to exhibit high-efficiency translation or high-visibility two-photon interference for many different shapes of input wave packets or for only a few input wave packets, respectively. Also, for a particular case, the Schmidt mode set was found to be nearly equal to a Hermite-Gaussian function set. The methods and results also apply with little modification to frequency conversion by sum-frequency conversion in optical crystals.