delicacy vs elegance

delicacy and elegance both are nouns.

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

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

delicacy (noun)	elegance (noun)
the quality of being beautiful and delicate in appearance	a refined quality of gracefulness and good taste
subtly skillful handling of a situation	a quality of neatness and ingenious simplicity in the solution of a problem (especially in science or mathematics)
lack of physical strength
slenderness
lightness in movement or manner
refined taste; tact
something considered choice to eat