writing vs notation

writing and notation both are nouns.

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

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

writing: the activity of putting something in written form
notation: the activity of representing something by a special system of marks or characters

Other hyponyms of writing include coding, cryptography, secret writing, steganography, handwriting, inscription.

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

writing: letters or symbols that are written or imprinted on a surface to represent the sounds or words of a language
notation: a technical system of symbols used to represent special things

writing (noun)	notation (noun)
the activity of putting something in written form	the activity of representing something by a special system of marks or characters
the act of creating written works	a technical system of symbols used to represent special things
the work of a writer; anything expressed in letters of the alphabet (especially when considered from the point of view of style and effect)	a comment or instruction (usually added)
letters or symbols that are written or imprinted on a surface to represent the sounds or words of a language
(usually plural) the collected work of an author