contact vs engagement

contact and engagement both are nouns.

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

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

Other hyponyms of contact include collision, hit, interlocking, mesh, meshing, flick, impact, touch, touching.

contact (noun)	engagement (noun)
the act of touching physically	the act of sharing in the activities of a group
close interaction	a hostile meeting of opposing military forces in the course of a war
(electronics) a junction where things (as two electrical conductors) touch or are in physical contact	the act of giving someone a job
a thin curved glass or plastic lens designed to fit over the cornea in order to correct vision or to deliver medication	employment for performers or performing groups that lasts for a limited period of time
a channel for communication between groups	a mutual promise to marry
a communicative interaction	contact by fitting together
the physical coming together of two or more things	a meeting arranged in advance
a person who is in a position to give you special assistance
the state or condition of touching or of being in immediate proximity

contact (verb)	engagement (verb)
be in or establish communication with
be in direct physical contact with; make contact