"Tanakh" is a Hebrew abbreviation for "torah" (the five books of Moses), "nevi'im" (prophets), and "ketuvim" (writings -- all the other books). While "tanakh" and "old testament" describe similar collections of scripture (there are some variations about which books are included between Jews and Christians and among Christians), the "tanakh" tag should be used for questions with a Jewish or neutral context and the "old testament" tag should be used for questions with a specifically-Christian context. For example:
Use "tanakh" for:
* What is the significance of the various divine names?
* Is "kill" the right word in the ten commandments?
* What is the tree of life in Proverbs?
* How do we understand "sin offerings" for things like giving birth? Does that involve "sin"?
* Who is "satan" in the book of Job?
Use "old testament" for:
* Where do the prophets foreshadow Jesus? Is that what Isaiah's suffering servant is about?
Possibly use both tags for:
* Does "almah" mean "virgin"?
For questions specifically about how Christian scripture reinterprets the Tanakh, see nt-use-of-the-ot.
See also: Wikipedia page on Tanakh