naval battle vs engagement

naval battle and engagement both are nouns.

Word	Noun	Adjective	Verb	Adverb
naval battle	Yes	No	No	No
engagement	Yes	No	No	No

As nouns, engagement is a hypernym of naval battle; that is, engagement is a word with a broader meaning than naval battle:

naval battle: a pitched battle between naval fleets
engagement: a hostile meeting of opposing military forces in the course of a war

Other hypernyms of naval battle include battle, conflict, fight.

naval battle (noun)	engagement (noun)
a pitched battle between naval fleets	the act of sharing in the activities of a group
	a hostile meeting of opposing military forces in the course of a war
	the act of giving someone a job
	employment for performers or performing groups that lasts for a limited period of time
	a mutual promise to marry
	contact by fitting together
	a meeting arranged in advance