commentary vs notation

commentary and notation both are nouns.

Word	Noun	Adjective	Verb	Adverb
commentary	Yes	No	No	No
notation	Yes	No	No	No

As nouns, notation is a hyponym of commentary; that is, notation is a word with a more specific, narrower meaning than commentary:

commentary: a written explanation or criticism or illustration that is added to a book or other textual material
notation: a comment or instruction (usually added)

Other hyponyms of commentary include Midrash, annotation, note.

commentary (noun)	notation (noun)
a written explanation or criticism or illustration that is added to a book or other textual material	the activity of representing something by a special system of marks or characters
	a technical system of symbols used to represent special things
	a comment or instruction (usually added)