"Twilight" occurs when the sun has set, but remains a small distance below the horizon. The word comes from Middle Englsh and means "half-light." "Dusk" is the latter and darker stage of twilight, occurring right before nightfall.
American Heritage Dictionary, 1978
According to Webster’s Dictionary twilight is the diffused light from the sky during the early evening or early morning when the sun is below the horizon and its light is refracted by the earth's atmosphere. It is also described as the time of the day when the sun is just below the horizon, especially the period between sunset and dark.According to the US Military Definition "Twilight is the period of incomplete darkness following sunset and preceding sunrise. Twilight is designated as civil, nautical, or astronomical, as the darker limit occurs when the center of the sun is 6 degrees, 12 degrees, or 18 degrees, respectively, below the celestial horizon. Dusk or civil dusk is the time at which the sun is 6 degrees below the horizon in the evening." At this time objects are distinguishable and some stars and planets are visible to the naked eye. Nautical dusk is when the sun is 12 degrees below the horizon in the evening. At this time, objects are no longer distinguishable, and the horizon is no longer visible to the naked eye. Astronomical dusk is the time at which the sun is 18 degrees below the horizon in the evening. At this time the sun no longer illuminates the sky, and thus no longer interferes with astronomical observations. Dusk should not be confused with sunset, which is the moment when the trailing edge of the Sun itself sinks below the horizon.