One definition for Primary source is a source that originates at the time of an event, a witness to the event in their own words. With that definition, a Secondary source is than a later witness or commentary on those first artifacts. In this case primary sources would include: letters, newspapers, diaries, interviews, and artifacts. Secondary sources would then be interpretations of those artifacts.
This gets tricky within some disciplines. For example, in Biblical studies some might call the Bible a primary source. It is, in that it is the witness to the events and leaves out interpretation/commentary. But for some scholars, translators, our English Bible is a secondary source because the primary is the Bible in the original languages (Greek, Hebrew, and Aramaic). To make it worse, some even argue that the Greek New Testament is a secondary source. For the text critic, the actual manuscripts and fragments are the primary and the edited UBS or Nestle-Aland is a secondary source. The ESV or NRSV would then be a tertiary source. And don't get me started about the footnotes in your English bible. I told you it gets tricky.
In Church history, at the undergraduate level at least, if you are reading the work of the original author, even in translation, it is often considered a primary source. This is especially true if you are using a "critical" edition of the work. A secondary source includes commentary or leaves out portions of the original.
Some other examples of primary sources: novels, plays, poems, movies and videos, paintings or photos, newspapers, speeches, memoirs, diaries, letters (even texts, IMs, emails and SnapChat!!), interviews, census records, and obituaries.
Most instructors want their students to approach primary sources uncluttered by commentary. The task of the student is to grasp the ideas and then synthesize those ideas with the works of other secondary interpreters. The student's work then becomes a new secondary sources.
These terms are all basically the same idea. The idea being that a published work has gone through a process in which the work was evaluated for quality and contribution to scholarship and then edited.
The publication process is something like this:
1 - author submits article to journal (general editor)
2 - general editor submits copies to two or three experts in the same field as the article
3 - the experts (peers or referees) then evaluate the article on contribution to scholarship, originality, and currency (among other specifics for the journal and discipline).
4 - the experts then return the article to the general editor for either publication or rejection.
5 - the general editor then sends a rejection letter to the author, returns article to author for editing/changing certain points in article (back to start), or edits for publication.
The timeframe from submission to publication varies by journal. It is rarely less than one year.
The editorial and peer review process elevates the quality of the article.
Case Study - A case study may be published as a journal article or as an entire monograph. A case study is the detailed report and evaluation of some event or organization. The case study will include great deals of context and methodology as well as the conclusions of the researchers.
Conference Report or Proceedings - A conference report or proceeding is a written form of a presentation or all the presentations given at a conference. These are often edited versions of the oral presentation. It is not uncommon to see a journal article that is nearly the same as a conference report from a year or two earlier.
Journal (trade or scholarly) - A journal is a periodical that is meant for a specific audience and is typically for educational purposes. A trade journal is intended for people that work in that industry. A scholarly journal is one that intended for academics (students, professors, and independent scholars).
Literature Review - A literature review is an extended writing that focuses on summarizing the state of research in one area. The review itself is often a summary of as many of the articles and books written over a certain timeframe. This is a great way to create a bibliography of works on a subject.
Magazine - A magazine is a periodical that is meant for a general audience and is typically for entertainment or hobby.
Monograph - A monograph is a writing (graphe) on one (monos) subject. A detailed book about one subject is a monograph.
Periodical - A periodical is a written source that is issued/published periodically. Newspapers are published daily, journals and magazines may be published monthly or quarterly, and some reports or government papers are issued annually.
Reference - Reference are books that are used for quick introductory research, not in-depth. Reference materials include dictionaries, encyclopedias, lexicons, atlases, and such. They are often produced by many people under the direction of one general editor.
Serial - A serial publication is one that is meant to be viewed as one work that is published in many parts. The time between publications may vary, but all the parts are meant to be taken as a whole. The word "series" many appear in the subtitle if it is a book series.
Theses and Dissertations - Theses are papers written at the end of either a Masters degree or a doctorate. A dissertation is typically the name for the paper at the end of a Doctorate of Philosophy (PhD) program. These papers are very detailed, have great depth of research and typically are very current in their research.
White Paper - A white paper is a document which intends to persuade the reader to the point of view of the author. Typically a white paper is a proposal about a change and it includes the logic and evidence to support that idea. White papers can be government documents or business proposals or from other organizations.
Working Paper - An early version of a future publication. It is not uncommon for a researcher to "publish" a working paper announcing their research ideas in hopes of receiving critical responses. Those responses will be taken into consideration and answered in the final published journal article. Often similar to a paper delivered at a conference.