scarlet letter vs emblem

scarlet letter and emblem both are nouns.

Word	Noun	Adjective	Verb	Adverb
scarlet letter	Yes	No	No	No
emblem	Yes	No	No	No

As nouns, emblem is a hypernym of scarlet letter; that is, emblem is a word with a broader meaning than scarlet letter:

scarlet letter: the letter A in red; Puritans required adulterers to wear it
emblem: a visible symbol representing an abstract idea

Other hypernyms of scarlet letter include allegory.

scarlet letter (noun)	emblem (noun)
the letter A in red; Puritans required adulterers to wear it	special design or visual object representing a quality, type, group, etc.
	a visible symbol representing an abstract idea