symbol vs dollar sign

symbol and dollar sign both are nouns.

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

As nouns, dollar sign is a hyponym of symbol; that is, dollar sign is a word with a more specific, narrower meaning than symbol:

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

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