The Chicago and Turabian styles are almost the same. Turabian is a simplified version of Chicago, and includes advice about writing. Chicago style is intended for works for publication. Turabian style is more pared down and intended for papers, dissertations and theses that are not intended for commercial publication.
There are just a few very slight differences between the styles, for example, Chicago leaves it up to the writer to decide whether to include the date accessed for a website; Turabian requires it.
Both styles have two citation systems: Author/Date and Notes/Bibliography. Author/date is more common in the sciences and social sciences and uses in-text, parenthetical citation of sources with a reference list at the end, Notes/Bibliogaphy is common in the humanities, uses footnotes, and includes a reference list (bibliography) at the end of the work.
“Many journal articles are available online, often through your school’s library website or from a commercial database. To cite an article that you read online, include both an access date and a URL. If a URL is listed along with the article, use that instead of the one in your browser’s address bar. If you consulted the article in a library or commercial database, you may give the name of the database instead.” (p182, Turabian 8th edition)
"…some sources are identified by a DOI (digital object identifier). URLs based on DOIs are more persistent and stable than ordinary URLs. To cite a source that includes a DOI, append the DOI to https://dx.doi.org/ in you citation. For examples, see the sections on journal articles in figure 16.1 (for bibliography style) or figure 18.1 (for author-date style) and in chapters 17 and 19.” (p141, Turabian 8th edition)