engage vs pursue

engage and pursue both are verbs.

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

As verbs, engage and pursue are synonyms defined as:

engage and pursue: carry out or participate in an activity; be involved in

Other synonyms of engage include prosecute.

engage (verb)	pursue (verb)
get caught	go in search of or hunt for
consume all of one's attention or time	follow in or as if in pursuit
give to in marriage	carry out or participate in an activity; be involved in
keep engaged	carry further or advance
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)