importance vs emphasis

importance and emphasis both are nouns.

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

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

Other hyponyms of importance include accent, primacy.

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