dollar sign vs symbol

dollar sign and symbol both are nouns.

Word	Noun	Adjective	Verb	Adverb
dollar sign	Yes	No	No	No
symbol	Yes	No	No	No

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

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

dollar sign (noun)	symbol (noun)
a mark ($) written before a number to indicate that it stands for the number of dollars	something visible that by association or convention represents something else that is invisible
a symbol of commercialism or greed	an arbitrary sign (written or printed) that has acquired a conventional significance