engagement vs ringing

engagement and ringing both are nouns.

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

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

engagement (noun)	ringing (noun)
the act of sharing in the activities of a group	having the character of a loud deep sound; the quality of being resonant
a hostile meeting of opposing military forces in the course of a war	the giving of a ring as a token of engagement
the act of giving someone a job	the sound of a bell ringing
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