Holy Mother Church distinguishes between vigil Masses and anticipatory Masses. True vigil Masses are celebrated only on specific feast days: Christmas, Easter, Ascension (where celebrated on the Thursday after the Sixth Sunday after Easter), Pentecost, St. John the Baptist, Sts. Peter and Paul, and the Assumption of the Blessed Virgin Mary.
All other Masses celebrated on the previous afternoon or evening as fulfilling the Sunday obligation are really anticipatory Masses.
The difference between them is that vigil Masses have propers of their own. Anticipatory Masses use the propers of the next day’s Masses.
Propers are texts of the Mass that vary according to the date, such as the Responsorial. By contrast, the ordinary or commons, are texts that remain the same at every Mass, such as the Creed.
Sunday Masses, and other Masses on the day itself, are preferred over vigil or anticipatory Masses. However, where good reason exists for a parishioner to attend the vigil or anticipatory Mass, it completely fulfills his Mass obligation for that day.
The question often arises, especially among Hebrew Catholics, whether the vigil Mass is permitted because of the Jewish calendar, which begins every day at sunset. The best answer I know comes from Fr. Edward McNamara, a professor of liturgy at Regina Apostolorum university, in his article, Saturday Mass for Sunday.