Cross reference is a reference to information located somewhere else in the same document.  So if in Chapter 3 of a book, the reader is referred to Appendix A for more detailed information on a specific topic, that’s a cross reference. Also, if you use MLA format, a cross-reference is a way to reference multiple articles in an edited work.  In MLA, you can include the full citation for the edited book itself in the reference list, and then for each article, just list the author, article title, last name(s) of the editor(s), and the page numbers for the article. 

A secondary citation is a reference to a work that was referenced in a different document, but that you did not actually read yourself.  For example, you are reading a new book by Tom Jones that includes a description of a study by John Smith.  You want to discuss Smith’s work in a paper you are writing but don’t have access to his report; you only know about his study because you read about it in the book by Jones.  So your reference to Smith is a secondary citation.  In your paper, you would say something like, “According to research by Smith (as cited in Jones, 2015), ……..”

I would define secondary citation as a supporting reference based not on the actual article cited, but another document which cited this original article. Therefore, secondary citation risks repeating any error made by the reference document in either the citation or the information therein.

I would understand a cross-reference to be a reference to one already listed within a particular document.

Cross reference is a reference to information located somewhere else in the same document.  So if in Chapter 3 of a book, the reader is referred to Appendix A for more detailed information on a specific topic, that’s a cross reference. Also, if you use MLA format, a cross-reference is a way to reference multiple articles in an edited work.  In MLA, you can include the full citation for the edited book itself in the reference list, and then for each article, just list the author, article title, last name(s) of the editor(s), and the page numbers for the article. 

A secondary citation is a reference to a work that was referenced in a different document, but that you did not actually read yourself.  For example, you are reading a new book by Tom Jones that includes a description of a study by John Smith.  You want to discuss Smith’s work in a paper you are writing but don’t have access to his report; you only know about his study because you read about it in the book by Jones.  So your reference to Smith is a secondary citation.  In your paper, you would say something like, “According to research by Smith (as cited in Jones, 2015), ……..”

Nothing more to add.  Ellen Cohn said it exactly right.  Kudos.

a document which refers to associated information elsewhere in the document itself

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Yes Ramon, absolutely - I totally agree with David's statement.  Any time you make a secondary citation you are risking perpetuating an error. In my example, if Jones incorrectly described Smith's research, your discussion could repeat Jones' errors.

Thank you Ellen, for giving a much more instructive answer than mine. All I would add, is to be very wary of copying references from another document without first checking against the original. For example, a study of the accuracy of references published in top-tier medical journals found high error rates in BMJ (17%), JAMA (28%) and The Lancet (40%). While most were minor spelling mistakes, 20 cited the wrong journal or publication year, 15 the wrong volume, and 50 the wrong page, all of which would hinder retreival of the cited article and prevent automatic linking to the reference.

http://www.thelancet.com/journals/lancet/article/PIIS0140-6736%2805%2974090-3/fulltext

Thanks, David.  I totally agree about the need to double check references against the original because of the possibility of errors.  I do citation analysis research in criminal justice and find all sorts of errors, including misspelled authors' names, omitted authors, incorrect initials, you name it.  

I recall a regularly updated guideline that cited the wrong paper altogether. It took a long search to find the correct reference based on a few approximate data values in one sentence. In such cases, I'd recommend contacting the corresponding author so that the mistake can be rectified and avoid putting others to the same trouble.

Thanks for the explanation Ellen. Well appreciated. What do have to say about footnotefootnotes? Is it the same as cross reference?

As Ellen explained so well, cross-references lead the reader to another reference or other supporting information within the document relating to a certain point. Footnotes, either at the bottom of a page or table, or the end of a document, provide detail, explanation or caveats to help readers better understand the information.

Good Question  and good answer from Ellen G. Cohn

Please could somebody provides an example shows the difference between the two types ?

Another issue is that information in the primary source may have been updated, eg, in the case of guidelines, making it inaccurate, or the paper may even have been retracted, discrediting its reliability. This does happen, as discussed in interesting articles here:

http://retractionwatch.com/2017/04/05/citations-retracted-papers-dont-note-theyre-problematic-authors-say/

https://qz.com/583497/researchers-keep-citing-these-retracted-papers/

If within the same document i refer to a related information elsewhere in the same document, then i am cross-referencing