notation vs commentary

notation and commentary both are nouns.

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

As nouns, commentary is a hypernym of notation; that is, commentary is a word with a broader meaning than notation:

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

Other hypernyms of notation include comment.

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