cross-purpose vs intention

cross-purpose and intention both are nouns.

Word	Noun	Adjective	Verb	Adverb
cross-purpose	Yes	No	No	No
intention	Yes	No	No	No

As nouns, intention is a hypernym of cross-purpose; that is, intention is a word with a broader meaning than cross-purpose:

cross-purpose: a contrary aim
intention: an anticipated outcome that is intended or that guides your planned actions

Other hypernyms of cross-purpose include aim, design, intent, purpose.

cross-purpose (noun)	intention (noun)
a contrary aim	an act of intending; a volition that you intend to carry out
	an anticipated outcome that is intended or that guides your planned actions
	(usually plural) the goal with respect to a marriage proposal