symbol vs emblem

symbol and emblem both are nouns.

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

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

symbol: something visible that by association or convention represents something else that is invisible
emblem: a visible symbol representing an abstract idea

symbol (noun)	emblem (noun)
something visible that by association or convention represents something else that is invisible	special design or visual object representing a quality, type, group, etc.
an arbitrary sign (written or printed) that has acquired a conventional significance	a visible symbol representing an abstract idea