call-back vs engagement

call-back and engagement both are nouns.

Word	Noun	Adjective	Verb	Adverb
call-back	Yes	No	No	No
engagement	Yes	No	No	No

As nouns, engagement is a hypernym of call-back; that is, engagement is a word with a broader meaning than call-back:

Other hypernyms of call-back include employment.

call-back (noun)	engagement (noun)
the recall of an employee after a layoff	the act of sharing in the activities of a group
a return call	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