mistaking vs imbroglio

mistaking and imbroglio both are nouns.

Word	Noun	Adjective	Verb	Adverb
mistaking	Yes	No	No	No
imbroglio	Yes	No	No	No

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

Other hyponyms of mistaking include misconstrual, misconstruction, misreading.

mistaking (noun)	imbroglio (noun)
putting the wrong interpretation on	a very embarrassing misunderstanding
	an intricate and confusing interpersonal or political situation