patriarchy vs patriarchate

patriarchy and patriarchate both are nouns.

Word	Noun	Adjective	Verb	Adverb
patriarchy	Yes	No	No	No
patriarchate	Yes	No	No	No

As nouns, patriarchy and patriarchate are synonyms defined as:

patriarchy and patriarchate: a form of social organization in which a male is the family head and title is traced through the male line

patriarchy (noun)	patriarchate (noun)
a form of social organization in which a male is the family head and title is traced through the male line	a form of social organization in which a male is the family head and title is traced through the male line
	the jurisdiction of a patriarch