Having made some comments myself around here recently using "commentary" in a rather broad, perhaps sloppy, sense*, in effect for any "interpretation"; and having noticed the excellent points being brought out in the current thread " 'some say…' " (), here's some potential clarification – extracted to a new thread to avoid hijacking another thread.
The status of my current understanding (open to correction):
Strictly speaking, a "commentary" (in the Pali Canon, in Confucian texts, Christian texts, etc.) is a work that follows some original text and, more or less line-by-line, trying to explain tries it in more detail. In the Pali tradition, these are called Atthakathā **. For instance the Majjhima Nikaya Atthakatha, (abbreviation MA) is "the" commentary on the Majjhima Nikaya. I believe "the" commentaries always treat basic texts in one of the three "baskets" (Tipitaka). For instance, Buddhaghosa's commentary on the Dhammasangani (1st book of Abhidhamma), the Atthasālinī, is titled in its English translation as "The Expositer" – commentary as exposition.
Then a "sub-commentary" (Pali "Tikā") is an exposition of a commentary, and hence, perhaps, of the original text. The official "sub-commentaries" I guess (haven't, yet, read any) each relate to one of the official canonical commentaries.
One sees this in the major subdivisions of the CST4.0 version of the Pali Canon:
1) Tipitaka – the "3 baskets"
2) Atthakathā – the commentaries, on (1)
3) Tikā – the sub-commentaries, on (2)
4) Añña "other" – e.g. the Visuddhimagga
Where both (2) and (3) have 3 subdivisions: "Sutta Pitaka", "Vinayapitaka", and "Abhidhamma Pitaka". (Why the second one runs the two words together beats me.)
One finds clear understanding of this organization occasionally. For instance, Pa Auk Sayadaw (in the interview in Richard Shankman's book on Samadhi), lists them in passing:
"People should trace back to the original suttas, the original commentaries and subcommentaries, and then to the Visuddhimagga, and only then will they understand the meanings."
There are also other (non Canonical) commentaries written by various authors down through the ages and into the present. For instance, the works (writings and transcribed talks) of Mahasi Sayadaw include 15 or so "Discourses" on individual sutta-s; though some of these include a lot more than just following the sutta text – e.g. his discourse on the Dhammacakkapavattana Sutta. I've heard there is a commentary on the Vissudhimagga. I'm Not sure how books like the Abhidhammamattha-Sangaha (which B.Bodhi translated as "A Comprehensive Manual of Abhidhamma") would be classified.
Then there's the term "the commentarial tradition", which it seems more diffuse, as people (including myself) use it a lot without defining exactly. Does it refer to a specific, well-defined body of texts? Or does it include an on-going tradition of glossing ancient texts – as, for example, both Mahasi Sayadaw's great "Treatise on Vipassana / Manual of Insight" and Daniel Ingram's "Mastering the Core Teachings of the Buddha" might be considered modern commentaries on the Visuddhimagga.
* In "Suttas and Commentaries. Was: Bhante Jag - Euthanasia", I wrote:
"I suspect "commentary" automatically gets carried down in any tradition, as person-to-person transmission involves, almost by definition, "commentary" – more detailed explanation – by the teacher. The writings of Mun-Lee-Chah-etc, as well as those of the PaAuk or Mahasi Sayadaws are all "commentaries". "
** PTS Dictionary:
Attha – "… 3. sense, meaning,…"
kathā -- "… 5 explanation, exposition, in Attha-…"