engage vs vow

engage is not a noun while vow is a noun.

Word	Noun	Adjective	Verb	Adverb
engage	No	No	Yes	No
vow	Yes	No	Yes	No

As verbs, vow is a hypernym of engage; that is, vow is a word with a broader meaning than engage:

engage (noun)	vow (noun)
	a solemn pledge (to oneself or to another or to a deity) to do something or to behave in a certain manner

engage (verb)	vow (verb)
get caught	make a vow; promise
consume all of one's attention or time	dedicate to a deity by a vow
give to in marriage
keep engaged
engage for service under a term of contract
hire for work or assistance
ask to represent; of legal counsel
engage or hire for work
carry out or participate in an activity; be involved in
carry on (wars, battles, or campaigns)