Dogmas are revealed truths which have been formally defined or proposed by the Church. For example, the Vatican Council (opened on 8 December, 1869) defined Papal Infallibility as
"a divinely revealed dogma" when "the Roman Pontiff speaks ex
cathedra [...]".
Please note that the dogmas of the Church are immutable. [cf. Dogma | New Advent].
“Doctrine” simply means “teaching”. Thus when children are preparing to receive their first Holy Communion, a book such as A Catechism3 of Christian Doctrine - (going by the New Advent article, this = A Teaching of Christian Teaching) - may be utilized. [cf. Christian Doctrine | New Advent].

Pope St. John Paul II [the Great], in his Apostolic Constitution Fidei Depositum on the Publication of the Catechism of the Catholic Church, wrote:
3. The Doctrinal Value of the Text
The Catechism of the Catholic Church, which I approved 25 June last and the publication of which I today order by virtue of my Apostolic Authority, is a
statement of the Church's faith and of catholic doctrine, attested
to or illumined by Sacred Scripture, the Apostolic Tradition and the
Church's Magisterium. I declare it to be a sure norm for teaching the
faith and thus a valid and legitimate instrument for ecclesial
communion. May it serve the renewal to which the Holy Spirit
ceaselessly calls the Church of God, the Body of Christ, on her
pilgrimage to the undiminished light of the Kingdom!
- To answer Infallible statement and Infallible papal teaching an understanding is required on
Infalliblity (cf. Infallibity | New advent)
In general, exemption or immunity from liability to error or failure; in particular in theological usage, the supernatural
prerogative by which the Church of Christ is, by a special Divine
assistance, preserved from liability to error in her definitive
dogmatic teaching regarding matters of faith and morals.
Thus in the Church, an infallible statement is a statement regarding faith and morals that has been preserved from liability to error.
And an infallible papal teaching is a papal teaching in faith and morals that has been preserved from liability to error.
- To answer Statement made ex cathedra an understanding is required on
Ex Cathedra (cf. Ex Cathedra | New Advent)
Literally "from the chair", a theological term which signifies
authoritative teaching and is more particularly applied to the
definitions given by the Roman pontiff.
Therefore statements made ex cathedra are those made "from the chair".
- Definitively proposed doctrine (= definitively proposed "teaching") means a proposed doctrine/teaching that is to be firmly accepted and held by all the Church's faithful, i.e., they are binding on all the faithful. For example,
In his Apostolic Letter Ordinatio Sacerdotalis to the Bishops of the Catholic Church on Reserving Priestly Ordination to Men Alone, Pope St. John Paul II [the Great] wrote:
this judgment is to be definitively held by all the Church's faithful.
cf. Ad Tuendam Fidem - John Paul II - Apostolic Letter Motu Propio (18 May 1998):
Canon 750 of the Code of Canon Law
§ 2. Furthermore, each and everything set forth definitively by the
Magisterium of the Church regarding teaching on faith and morals must
be firmly accepted and held; namely, those things required for the
holy keeping and faithful exposition of the deposit of faith;
therefore, anyone who rejects propositions which are to be held
definitively sets himself against the teaching of the Catholic Church.
cf. CCC 892 Divine assistance is also given to the successors of
the apostles, teaching in communion with the successor of Peter, and,
in a particular way, to the bishop of Rome, pastor of the whole
Church, when, without arriving at an infallible definition and without
pronouncing in a "definitive manner," they propose in the exercise of
the ordinary Magisterium a teaching that leads to better understanding
of Revelation in matters of faith and morals. To this ordinary
teaching the faithful "are to adhere to it with religious
assent"LG 25. which, though distinct from the assent of
faith, is nonetheless an extension of it.
My understanding is that this is a statement by one in authority, in this case, statements by Bishops in communion with the Pope, when they make such a statement in the course of their ordinary teaching of the faithful. The faithful are to adhere to such a statement with religious assent.
Are any of these the same? No as shown above.
Are all infallible statements papal teachings? No they are not. Infallible papal teachings are part and a subset of the infallible teaching of the Church.
Are all doctrines dogmas? No. Dogmas when taught are doctrines or again, doctrine contains (teaches) dogma, and doctrines which are revealed truths become dogmas when they are formally defined or proposed by the Church, and thereafter taught as [part of the] doctrine.
What exactly are the differences between these? See above.
Please see also: Profession of Faith | CDF. Please read the section: "Doctrinal Commentary
on the Concluding Formula of the Professio fidei".
1. dogma (n.) c.1600 (in plural dogmata), from Latin dogma "philosophical tenet," from Greek dogma (genitive dogmatos) "opinion, tenet," literally "that which one thinks is true," from dokein "to seem good, think" (see decent). Treated in 17c.-18c. as a Greek word in English.
2. doctrine (n.) late 14c., from Old French doctrine (12c.) "teaching, doctrine," and directly from Latin doctrina "teaching, body of teachings, learning," from doctor "teacher" (see doctor (n.)).
3. catechism (n.) c.1500, "instruction in Christian principles," also "elementary question-and-answer book of religious instruction," from French catéchisme (14c.) and directly from Church Latin catechismus "book of instruction," from Greek katekhismos, from katekhizein "to teach orally" (see catechize). Related: Catechismal.