Motu Proprio: A document issued Motu Proprio is from the Pope on his own initiative, and not in response to a request or at the initiative of others. Its legal determinations carry the full force of papal authority, though it does not derogate from existing laws unless specifically stated. It can be any category of document.
Apostolic Constitution: In teaching, it includes solemn Magisterial acts of the Pope; in governance, erecting dioceses, changing their status, rules for a papal election and the like.
Encyclical: A circular or general letter expressing the mind of the Pope, generally on matters of faith and morals. It may be a letter to the entire Church or an epistle to a particular Church or people (e.g. Mit brennenden sorge, Pius XI's encyclical to the German people condemning racism).
Apostolic Letter: Letters of less solemn authority than an encyclical, they may be written on a doctrinal matter (e.g. Pope John Paul II's Letter On the Beginning of the Third Millennium). They may also announce a papal act such as declaring a person Venerable (heroic virtue) or declaring a church a Basilica.
Apostolic Exhortation: A category of document similar to an Apostolic Letter, which Pope John Paul II uses to communicate to the Church the conclusions he has reached after consideration of the recommendations of a Synod of Bishops. He has also used it in other circumstances, such as to exhort religious to a deeper evangelical life.
Common Declaration: A joint statement of the Holy Father and another religious leader concerning a common understanding of some teaching.
Homily: The homilies of the Pope on the Scripture readings at Mass.
Discourse: In settings outside Mass (at which his address is called a homily) or outside the usual audience setting, the Pope may give a discourse to groups of people, upon arriving or departing a place, before or after Mass, at a rosary or in some circumstance not a homily or an audience.
Message: Written or spoken messages, often conveying a personal greeting, to individuals or groups. Usually briefer than a letter or an allocution.
A rather difficult site to navigate, the Vatican Library provides access to information about manuscripts, printed books, archives, incunabula, and coins and medals. Images for many items are available, and a major digitization project is in progress. Searching can be difficult if you don’t know exactly what it is you are looking for. There are links directly to digitized manuscripts and incunabula, though they are noted by abbreviations, so you’ll need to know what it is you’re looking for.
As associated site regarding the digitization project contains more usable links to some of the digitized manuscripts.
The Holy See site is enormous, and contains all sorts of information, including primary documents. Researchers can find biographical information about the current and past popes, as well as the documents produced during each of their terms. Documents are available in English translation and original languages of composition. Researchers are cautioned that there is a wealth of information here, and it is quite easy to get sidetracked or lost.
Some knowledge about the types of papal documents is required to efficiently search the site.