emphasis vs importance

emphasis and importance both are nouns.

Word	Noun	Adjective	Verb	Adverb
emphasis	Yes	No	No	No
importance	Yes	No	No	No

As nouns, importance is a hypernym of emphasis; that is, importance is a word with a broader meaning than emphasis:

Other hypernyms of emphasis include grandness.

emphasis (noun)	importance (noun)
intensity or forcefulness of expression	the quality of being important and worthy of note
the relative prominence of a syllable or musical note (especially with regard to stress or pitch)	a prominent status
special and significant stress by means of position or repetition e.g.
special importance or significance