And I don't mean to confuse you more - but in the third level (I agree that is a bad term, but I too can't think of a better one at the moment) of the encyclicals - it not just one. There are numerous levels of authority in the Pope's official writings (i.e., those not as a private theologian, like the Pope's book Jesus of Nazareth).
From this website:
Vatican documents include, in descending order of formal authority: apostolic constitutions, encyclical letters, encyclical epistles, apostolic exhortations, apostolic letters, letters and messages.Apostolic Constitutions:
Document of the highest authority, issued by the Pope, or by a Church Council with the Pope’s approval. Apostolic constitutions today have the authority of the ancient apostolic constitutions, a collection of laws from the late fourth century, which included 85 canons attributed to the Apostles dealing with ordinations, official responsibilities, and the moral behavior of bishops and priests. They eventually became the basis for canon law in the West.
When used to proclaim a Church dogma, called a Dogmatic Constitution. When used for pastoral teaching, called a Pastoral Constitution.Encyclical Letters:
A pastoral letter written by the Pope to the entire Church, generally concerning matters of doctrine, morals or discipline, or significant commemorations. Its formal title is the first few words of its official text, usually in Latin.
From the Latin encyclicus and the Greek enkyklios, circular.
Encyclicals are not divinely inspired and do not contain new revelation, but they are authoritative teaching instruments from the Vicar of Christ. In descending order of formal authority, the papal documents are: apostolic constitutions, encyclical letters, encyclical epistles, apostolic exhortations, apostolic letters, letters, and messages. An encyclical letter is written for the whole Church, while an encyclical epistle is directed toward part of the Church, e.g., bishops or laity in a particular country, leaders of religious orders, priests, etc.
The original Apostles, particularly St. Paul, used letters to keep in touch with far distant church communities. Twenty-one of these letters were included as part of the New Testament. After the Apostles passed into eternity, bishops often sent letters to one another, and sometimes to the faithful, to promote consistency in faith and discipline, especially about doctrines, feast-day celebrations, and liturgical calendars. The Bishop of Rome wrote epistles to bishops all over the world. He also received a great many letters from bishops all over the world and circulated them to other bishops.
The practice of circular letters fell into disuse during the Middle Ages, when the collegial bonds among bishops began to fray. The Holy See began to write letters to one bishop at a time concerning the affairs of his local diocese, and each diocesan bishop would in turn write only to the Holy See.
Pope Benedict XIV (1740-1758), helped by widespread use of the printing press, revived the ancient tradition of the Pope writing a common letter to all the bishops of the world; modern collections of papal letters usually begin with his papacy. Pope Gregory XVI (1831-1846) called these letters encyclicals, from the Latin encyclicus, circular, because they were intended for wide circulation. However, for papal letters published between 1740 and 1870, there was no agreement among scholars as to which were encyclicals. After Vatican I (1870) encyclical letters were clearly marked as such.
Pope Leo XIII (1878-1903) restored an important characteristic of the early Christian circular letters. Encyclicals since 1740 had been primarily admonitions and exhortations regarding traditional issues; Pope Leo XIII addressed new substantive issues, such as Catholic social teaching. He wrote some seventy-five encyclicals, including such classics as Humanum Genus (1884) on Freemasonry, Rerum Novarum (1891) on Catholic social teaching, and Providentissimus Deus (1893) on Holy Scripture, and Annum Sacrum (1899) on consecration to the Sacred Heart.
During the twentieth century, Pope Pius X (1903-1914) wrote sixteen encyclicals, Pope Benedict XV (1914-1922) wrote twelve, Pope Pius XI (1922-1939) wrote thirty, Pope Pius XII (1939-1958) wrote forty-one, Pope John XXIII (1958-1963) wrote eight, Pope Paul VI (1963-1978) wrote seven, and Pope John Paul II has so far written thirteen.
Since 1740 the Popes have produced nearly three hundred encyclicals, most of no continuing pastoral or theological interest. Pope Benedict XIV’s Quod Provinciale (1754) to the Bishops of Albania on the use of Islamic names by Christians, and Pope Leo XIII’s In Amplissimo (1902) thanking the American bishops for their good wishes on his anniversary, address no pressing needs for the Church Militant of our day. Indeed, among the encyclicals written before Pope John Paul II, perhaps ten percent are currently studied by faithful theologians.
Pope John Paul II’s encyclical letters have had a powerful impact on Church and also on non-Catholics via the public media, such as Laborem Exercens (1981) and Centesimus Annus (1991) on Catholic social teaching, Veritatis Splendor (1993) on the splendor of the truth, Evangelium Vitae (1995) on the value of human life, Ut Unum Sint (1995) on ecumenism, and Fides et Ratio (1998) on the unity of faith and reason.Encyclical Epistles:
A letter written by the Pope to part of the Church, e.g., bishops or laity in a particular country, leaders of religious orders, priests, etc.. From the Latin encyclicus and the Greek enkyklios, circular.
Because encyclical epistles are directed to a particular audience within the Church, they receive a great deal of attention from those who whom they are directed. Naturally, however, they receive little attention from those outside the audience to which they are directed.
A recent example would be Pope John Paul II’s encyclical epistle, Slavorum Apostoli on evangelization of the Slavic peoples by Saints Cyril and Methodius. It is addressed “to the bishops, priests, and religious families and to all the Christian faithful,” but certainly of more interest to the Slavic peoples than to the generality of Catholics.Apostolic Exhortations:
A letter written by the Pope to the Church encouraging its people to take some particular action.
Because apostolic exhortations do not define the development of doctrine, they are lower in formal authority than encyclical letters, which are directed to the whole Church and which may define development of doctrine.
A recent example would be Pope John Paul II’s apostolic exhortation, Ecclesia in America, January 22, 1999, encouraging the faithful to seek the living Christ and find conversion, communion and solidarity within the context of the Great Jubilee and the new evangelization.Apostolic Letters:
Document issued by the Pope or by a Vatican dicastery, usually for lesser appointments, erecting or dividing mission territory, designating basilicas, approving religious congregations, and other uses at a comparable level of importance.Letters:
A letter written by the Pope, the head of a dicastery, or other Vatican office to a Vatican official, the head of a religious order or other dignitary. The contents are of interest primarily to those to whom they are addressed. Pope John Paul’s letters of the year 2001 or even St. Paul’s letter to Philemon are examples.
Vatican offices also use letters to address points of doctrine or discipline that are not significant enough to require the Holy Father’s personal attention, or points that have already been addressed by the Holy Father but require clarification. These letters are often useful to active Catholics. A letter from the Pontifical Biblical Commission to Cardinal Suhard of January 16, 1948, Time of Pentateuch and Literary Form of First Eleven Chapters of Genesis, would be an example.Messages:
A letter written by the Pope or the head of a dicastery.
The contents are generally of transitory rather than permanent interest. Pope John Paul II’s messages are an example.