"An extraordinary form of the Roman Rite" is the term used in Pope Benedict XVI's motu proprio Summorum Pontificum for the liturgy of the 1962 Roman Missal, widely referred to as the "Tridentine Mass". The phrase indicates that the liturgy of the 1962 Missal, the celebration of which was permitted more widely by the motu proprio, differs from the normal present-day liturgy of the Roman Rite (the "ordinary form").
In the motu proprio, and in the accompanying letter that he sent to the Bishops, Pope Benedict designated the 1962 form an extraordinary form, not the extraordinary form of the Roman Rite, although the latter term has been adopted in certain quarters. The Pope wrote as follows:
The Roman Missal promulgated by Paul VI is the ordinary expression of the 'Lex orandi' (Law of prayer) of the Catholic Church of the Latin rite. Nonetheless, the Roman Missal promulgated by St. Pius V and reissued by Bl. John XXIII is to be considered as an extraordinary expression of that same 'Lex orandi'" (article 1 of the motu proprio)
The Missal published by Paul VI and then republished in two subsequent editions by John Paul II, obviously is and continues to be the normal Form – the Forma ordinaria – of the Eucharistic Liturgy. The last version of the Missale Romanum prior to the Council, which was published with the authority of Pope John XXIII in 1962 and used during the Council, will now be able to be used as a Forma extraordinaria of the liturgical celebration. It is not appropriate to speak of these two versions of the Roman Missal as if they were 'two Rites'. Rather, it is a matter of a twofold use of one and the same rite" (Letter of Pope Benedict XVI accompanying his motu proprio Summorum Pontificum).
Another example of the Holy See's use of the technical term "extraordinary" in liturgical contexts is the instruction Redemptionis Sacramentum, which insisted on the expression "extraordinary minister of Holy Communion", to the exclusion of terms such as “special minister of Holy Communion”. This 2004 instruction thus repeated the terminology used in canons 910 §2 and 943 of the 1983 Code of Canon Law, which, in the case of other sacraments also, insists on the distinction between the "ordinary" minister of the sacrament and those who in certain circumstances are allowed, by exception, to administer the sacrament.