What is the difference between a dogma, a doctrine, an infallible statement, an ex cathedra statement, etc.? There are a variety of terms used in the Catholic Church to refer to particular statements or beliefs. Here are a number of some such terms:


Dogma
Doctrine
Infallible statement
Infallible papal teaching
Statement made ex cathedra
Definitively proposed doctrine
Authoritative statement


Are any of these the same? Are all infallible statements papal teachings? Are all doctrines dogmas? What exactly are the differences between these?
Most of these terms are used interchangeably. So a clear cut definition may not be possible.


Doctrine: The official teachings of the Catholic church contained in the Word of God, written or handed down, and defined with a solemn judgment of the Church as divinely revealed truths. This may or may not be a dogma. Example, Mary, Co-Redemptrix
Dogma: Doctrines that are proclaimed formally by the Church as revealed in Scripture or Tradition. This may have been done by papal pronouncement (Pius IX: Immaculate Conception), by a Council (Chalcedon: Christ is two natures in one Divine Person). Those who do not believe in a Dogma, is considered to have left the church, on their own accord.
Statement made ex cathedra: This Literally means "Statement made from the chair". It is a theological term which signifies authoritative teaching and is more particularly applied to the definitions given by the Pope. I Vatican Council says that when Pope makes a statement ex cathedra, he does so in his office of pastor and doctor of all Christians. (Session IV, Const. de Ecclesiâ Christi, c. iv). Example: when declaring and defining a dogma, Pope makes that statement ex cathedra.
Infallible statement: Statements that are considered to be exempt or immune to error or failure; in particular in theological usage, by a special Divine assistance, church/pope is preserved from making an error when defining a dogma in the matters of faith and morals. All statements (with usual conditions) made by the Pope ex-cathedra are Infallible. But this is not necessarily reserved only to the pope. The teaching of the Magisterium of the Church are also considered infallible.
Definitively proposed doctrine: In simpler terms, this is implicitly accepted doctrines which are derived from previously revealed doctrines/dogmas. These are not articles of faith by themselves, but are necessary for faithfully keeping and expounding the deposit of faith. That is, if you do not believe them, then there might arise doctrinal inconsistency in faith. These doctrines may not have been officially proposed by the Church as formally revealed. And as it is usually the case, if some one inside the Church opposes its validity, these doctrines could, by dogmatic development, one day be declared to be revealed.


For example: The declaration of Pope Leo XIII in the Apostolic Letter Apostolicae Curae on the invalidity of Anglican ordinations. You don't have to believe that Anglican ordinations are invalid to be a catholic, but If you believe Anglican ordinations are valid ordinations, then there will be a problem with what you believe constitutes a valid ordination. As a valid ordination requires to be performed by a person with valid apostolic succession.
Other examples include doctrine that priestly ordination is reserved only to men, the teaching on the illicitness of prostitution, fornication and euthanasia.



On Infallible papal teaching and Authoritative statement, I don't have idea I am sorry. May be someone else can help.

Sources:


Summary of Categories of Belief in Professio fidei
Dogma (Catholic Encyclopedia)