written symbol vs symbol

written symbol and symbol both are nouns.

Word	Noun	Adjective	Verb	Adverb
written symbol	Yes	No	No	No
symbol	Yes	No	No	No

As nouns, symbol is a hypernym of written symbol; that is, symbol is a word with a broader meaning than written symbol:

written symbol: a written or printed symbol
symbol: an arbitrary sign (written or printed) that has acquired a conventional significance

written symbol (noun)	symbol (noun)
a written or printed symbol	something visible that by association or convention represents something else that is invisible
	an arbitrary sign (written or printed) that has acquired a conventional significance