symbol vs pound sign

symbol and pound sign both are nouns.

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

As nouns, pound sign is a hyponym of symbol; that is, pound 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
pound sign: a symbol for a unit of currency (especially for the pound sterling in Great Britain)

symbol (noun)	pound sign (noun)
something visible that by association or convention represents something else that is invisible	a symbol for a unit of currency (especially for the pound sterling in Great Britain)
an arbitrary sign (written or printed) that has acquired a conventional significance