different between discovery vs commentary

English

discovery (countable and uncountable, plural discoveries)

Something discovered.
This latest discovery should eventually lead to much better treatments for disease.
(uncountable) The discovering of new things.
The purpose of the voyage was discovery.
Automatic discovery of RSS feeds by a Web browser.
(countable, archaic) An act of uncovering or revealing something; a revelation.
- 1822, Alain René Le Sage, The Adventures of Gil Blas of Santillane
  Don Huberto actually fell in love with his kinswoman, and had presumption enough to declare his passion […] The lady being a woman of discretion, instead of making a discovery, which might have been attended with melancholy consequences, reprimanded her relation with gentleness […]
(law, uncountable) A pre-trial phase in which evidence is gathered.
The prosecution moved to suppress certain items turned up during discovery.
(law, uncountable) Materials revealed to the opposing party during the pre-trial phase in which evidence is gathered.
The defense argued that the plaintiff's discovery was inadequate.

From Middle French commentaire, from Latin comment?rius, comment?rium (“notebook”), compare French commentaire. See comment.

commentary (countable and uncountable, plural commentaries)

a series of comments or annotations; especially, a book of explanations or expositions on the whole or a part of some other work
- 1827, Henry Hallam, The Constitutional History of England
  This letter […] was published by him with a severe commentary.
(usually in the plural) a brief account of transactions or events written hastily, as if for a memorandum
an oral relation of an event, especially broadcast by television or radio, as it occurs

(series of comments or annotations): scholia (ancient & medieval European works); secondary source

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