The Magisterium teaches either infallibly or non-infallibly. All teachings of the Magisterium are either infallible, and therefore without the possibility of error, or non-infallible, having only a limited possibility of error (but never to such an extent as to lead the faithful away from the path of salvation). The Magisterium teaches infallibly in any of three ways:
1. Papal Infallibility – solemn definitions of the Pope
2. Conciliar Infallibility – solemn definitions of an Ecumenical Council
3. ordinary and universal Magisterium – when the Pope and the body of Bishops dispersed through the world are in agreement on one position, on a matter of faith or morals, definitively to be held.
All other teachings of the Magisterium, whether of the Pope alone, or an Ecumenical Council, or any group of Bishops, or an individual Bishop, are non-infallible. Moreover, the decisions of the temporal authority, which are rules and ruling, not teachings, are generally fallible (except for dogmatic facts).
Papal Infallibility is always a definition of doctrine. The term definition here is used in the theological sense, not in the vernacular sense. A doctrinal definition is a particular expression of an infallible teaching. The expression and the truth that it contains are without error. When the Pope teaches under Papal Infallibility, his teaching is termed a defining act. Such an act of the Magisterium is definitive, infallible, and irreformable.
The same is true for Conciliar Infallibility. The infallible teachings of an Ecumenical Council are doctrinal definitions. The Council teaches by a defining act, and the truth so taught is definitive, infallible, and irreformable.
All of the non-infallible teachings of the Church are taught by non-defining acts. In other words, when the Magisterium teaches non-infallibly, that act of the Magisterium is a non-defining act. It is not definitive; it is non-infallible and non-irreformable.
But an infallible teaching under the ordinary and universal Magisterium is a combination of the above two cases. It is an infallible, definitive, and irreformable teaching, and yet the teaching is not expressed by a defining act. There is no solemn definition; the infallible teaching does not have one particular form of expression as a definition. A teaching under the Universal Magisterium consists of a set of non-defining acts, which taken together form an infallible teaching.
A Pope or a Bishop teaches non-infallibly on a particular matter of faith or morals. Various other Popes and Bishops, over the course of time, teach the same doctrine, each by a non-infallible and non-irreformable act of the Magisterium. And each of these magisterial acts is non-defining. No single expression of that teaching is, by itself, a definition; no one act of the ordinary non-infallible Magisterium is a defining act.
Then, when the set of non-infallible teachings (non-defining acts) reaches a point whereby the set of authentic magisterial teachings on the same matter of faith and morals are in agreement, as one position definitively to be held, it becomes a single infallible teaching; it is no longer non-infallible. In this way, a set of non-defining acts expresses an infallible, definitive, and irreformable teaching, without a single solemn defining act.