engagement vs booking

engagement and booking both are nouns.

Word	Noun	Adjective	Verb	Adverb
engagement	Yes	No	No	No
booking	Yes	No	No	No

As nouns, booking is a hyponym of engagement; that is, booking is a word with a more specific, narrower meaning than engagement:

engagement: the act of giving someone a job
booking: the act of reserving (a place or passage) or engaging the services of (a person or group)

Other hyponyms of engagement include shape-up, call-back, reservation.

As nouns, engagement and booking are synonyms defined as:

engagement and booking: employment for performers or performing groups that lasts for a limited period of time

engagement (noun)	booking (noun)
the act of sharing in the activities of a group	the act of reserving (a place or passage) or engaging the services of (a person or group)
a hostile meeting of opposing military forces in the course of a war	employment for performers or performing groups that lasts for a limited period of time
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