eagerness vs elan

eagerness and elan both are nouns.

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

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

Other hyponyms of eagerness include ardor, ardour, zeal.

eagerness (noun)	elan (noun)
prompt willingness	enthusiastic and assured vigor and liveliness
a positive feeling of wanting to push ahead with something	distinctive and stylish elegance
	a feeling of strong eagerness (usually in favor of a person or cause)