designation vs delegacy

designation and delegacy both are nouns.

Word	Noun	Adjective	Verb	Adverb
designation	Yes	No	No	No
delegacy	Yes	No	No	No

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

Other hyponyms of designation include nomination, co-optation, co-option, ordinance, ordination, recognition.

designation (noun)	delegacy (noun)
the act of putting a person into a non-elective position	the appointment of a delegate
the act of designating or identifying something	a group of representatives or delegates
identifying word or words by which someone or something is called and classified or distinguished from others	the state of serving as an official and authorized delegate or agent