elan vs elegance

elan and elegance both are nouns.

Word	Noun	Adjective	Verb	Adverb
elan	Yes	No	No	No
elegance	Yes	No	No	No

As nouns, elegance is a hypernym of elan; that is, elegance is a word with a broader meaning than elan:

elan (noun)	elegance (noun)
enthusiastic and assured vigor and liveliness	a refined quality of gracefulness and good taste
distinctive and stylish elegance	a quality of neatness and ingenious simplicity in the solution of a problem (especially in science or mathematics)
a feeling of strong eagerness (usually in favor of a person or cause)