The following are some characterizations of source types found in a sample of books (selected by picking top results from a Google Books search on the phrase "tertiary sources"):
Some authors distinguish tertiary sources by their use of critical analysis, compared to simple summarization in secondary sources:
Primary source materials are original research papers written by the scientists who conducted the study.[...] Secondary source materials are papers or other documents that summarize the original work of others. [...] Examples of secondary source materials include a summary of previously published research in the introduction of a scientific research paper [...] Tertiary source materials consist of a systematic analysis, meta-analysis, or critical review of scientific papers. The boundaries between secondary and tertiary source materials are not hard and fast; rather, they merge from one into another and differ in the degree of critical analysis as the review moves from secondary to tertiary. The term itself has not been standardized. [...] Examples include papers or articles, like a critical review of all randomized clinical trials on a specific subject [...]. [p.44] Health Sciences Literature Review Made Easy, Judith Garrard. Jones & Bartlett Learning, Aug 4, 2016
Primary sources include conference proceedings, patents, dissertations, articles reporting the results of clinical trials, and other publications of original research. [...] Tertiary sources include information that has been compiled and repackaged, such as meta-analyses, practice guidelines, review articles, textbooks, encyclopedias, and Web sites. [...] Secondary sources are indexes that provide information about and access to primary and tertiary sources. The index of a textbook is an example of a secondary source [...]. [p. 55] Pharmacy Informatics. Philip O. Anderson, Susan M. McGuinness, Philip E. Bourne. CRC Press, Dec 1, 2009
Other authors, to the contrary, define tertiary sources as summaries lacking analysis or criticism:
Tertiary Source: Reference material that summarizes and condenses the information found in primary and secondary sources. [...] Information found in tertiary sources is collected, condensed, and combined from primary and secondary sources. The purpose of a tertiary source is to provide basic facts without analysis or criticism. [p. 57] Secondary Source: A summary, analysis, commentary, or criticism of events in history based on the study of primary sources relating to those events. [p. 85] Finding History: Research Methods and Resources for Students and Scholars. Christine Bombaro. Scarecrow Press, 2012
Some authors classify some types of reference works as secondary and others as tertiary:
Tertiary sources consist of general reference works and textbooks. [...] Secondary sources, literature used to identify and locate primary and other resources, consist of bibliographies, abstracting services, and indexing services. [p. 75] Remington: The Science and Practice of Pharmacy. David B. Troy, Paul Beringer. Lippincott Williams & Wilkins, 2006
Some authors classify encyclopedias and similar works as secondary sources, using the term tertiary source to refer to non-specialist summaries or summaries of summaries:
Secondary sources present secondhand information [...] collected, compiled, summarized, analyzed, synthesized, interpreted, and evaluated by someone studying primary sources. Journal articles, encyclopedia entries, and documentaries are typical examples of secondary sources. Tertiary Sources [...] are essentially reports of reports of research. Writers of tertiary sources are pulling together their own thoughts based on a reading of secondary sources. Examples of tertiary sources would include some articles in popular magazines and entries in Wikipedia. [pp. 35-36] The Research Writer, Spiral bound Version. John Van Rys, Verne Meyer, Patrick Sebranek. Cengage Learning, Jan 1, 2011
Secondary Sources: Secondary source is basically a material which has been selected, modified, arranged and organized according to some definite plan. [...] Secondary sources include: periodicals, bibliographies, indexing and abstracting journals, dictionaries and encyclopedias, handbooks, tables, formularies, reviews of progress, treatises, monographs, and textbooks. [...] Tertiary sources of information contain information thrice removed from the primary sources. [...] Tertiary sources may include: bibliography of bibliographies, guides to literature, list of research in progress, guides to libraries and sources of information, guide to organizations, etc. [p. 123] Scholarly Communication and the Publish or Perish Pressures of Academia. Munigal, Achala. IGI Global, Oct 17, 2016
Other authors base the distinction in part on the intended audience:
Secondary sources are books, articles, or reports that are based on primary sources and are intended for a scholarly or professional audience. [...] Tertiary Sources [...] are books and articles that synthesize and report on secondary sources for general readers, such as textbooks, articles in encyclopedias (including Wikipedia), and articles in mass-circulation publications like Psychology Today. The Craft of Research, Fourth Edition. Wayne C. Booth, Gregory G. Colomb, Joseph M. Williams, Joseph Bizup, William T. FitzGerald. University of Chicago Press, Oct 7, 2016
Conclusion: there is no generally accepted definition of what distinguishes secondary from tertiary sources.