The Tridentine Mass is the Mass from the Council of Trent (1545–1563), hence the name “Tridentine,” which was promulgated by Pope Saint Pius V (Quo Primum, 1570).
The Novus Ordo is the Mass from the Council of Vatican II (1962–1965) which was promulgated by Pope Paul VI (Novus Ordo, 1970).
The older Tridentine Mass was divided into two parts, the Mass of the Catechumens and the Mass of the Faithful. The Vatican II Novus Ordo Mass also has two halves, but calls them the Liturgy of Word and the Liturgy of the Eucharist instead.
The Tridentine Mass is celebrated only in Latin, while the Novus Ordo can be celebrated totally in Latin, totally in the vernacular, or with some parts in Latin and the rest in the vernacular.
Both have readings from Sacred Scripture (Bible) for either weekdays or weekends. Though not mandatory, the customary position for the celebrant is to be facing the people (versus populum) during the Liturgy of the Eucharist of the Novus Ordo. The Tridentine Mass mandated that the celebrant offer Mass ad orientem (toward the east) or ad apsidem (toward the apse or tabernacle) during the Mass of the Faithful. The Tridentine Mass has extra parts not present in the Novus Ordo, like the prayers at the foot of the altar (introibo ad altare Dei), at the offertory (Suscipe Sancta Trinitas), the last gospel, and prayers after low Mass (salve regina and prayer to Saint Michael). It also had many more signs of the cross for the priest to make and more elaborate rubrics depending on the solemnity of the Mass (high, solemn
Ecclesia Dei (1988) allowed wider and broader use of the Tridentine Mass for Roman Catholics, who felt it fulfilled their spiritual needs more than the Novus Ordo. Previously, it was rare to find a Tridentine Mass officially sanctioned by the local diocesan bishop after Vatican II, since Pope Paul VI wanted the new Mass to be the standard. The late Archbishop Marcel Lefebvre founded the Society of Saint Pius X in 1970, and they resisted the liturgical changes (to the Mass and the other sacraments) which originated from the Second Vatican Council. When Lefebvre illicitly consecrated bishops without papal mandate, he and those bishops incurred automatic excommunication and were in de facto schism. Pope John Paul II issued Ecclesia Dei, which also created the Priestly Fraternity of Saint Peter (FSSP) for those former members of the Society of Saint Pius X (SSPX) who wished to return to full communion with Rome. A renegade branch of the Pius X Society is the Pius V Society, which is ultra-traditional. Only religious communities in full communion with Rome, like the Fraternity of Saint Peter, are recognized by the Vatican and local dioceses to licitly celebrate the Tridentine Mass, as well as those Novus Ordo priests who obtain a mandate from their local diocesan bishop.
Byzantine Catholics use the Divine Liturgy of Saint John Chrysostom or the Divine Liturgy of Saint Basil, which is celebrated in Greek, Old Slavonic, Aramaic and vernacular languages.