emergency vs exigency

emergency and exigency both are nouns.

Word	Noun	Adjective	Verb	Adverb
emergency	Yes	No	No	No
exigency	Yes	No	No	No

As nouns, emergency and exigency are synonyms defined as:

emergency and exigency: a sudden unforeseen crisis (usually involving danger) that requires immediate action

Other synonyms of emergency include pinch.

emergency (noun)	exigency (noun)
a brake operated by hand; usually operates by mechanical linkage	a sudden unforeseen crisis (usually involving danger) that requires immediate action
a sudden unforeseen crisis (usually involving danger) that requires immediate action	a pressing or urgent situation
a state in which martial law applies	that which is required in a particular situation —usually used in plural.