discourse vs kerygma

discourse and kerygma both are nouns.

Word	Noun	Adjective	Verb	Adverb
discourse	Yes	No	Yes	No
kerygma	Yes	No	No	No

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

discourse: an address of a religious nature (usually delivered during a church service)
kerygma: preaching the gospel of Christ in the manner of the early church

Other hyponyms of discourse include baccalaureate, kerugma, evangelism, homily, preachment.

discourse (noun)	kerygma (noun)
an extended communication (often interactive) dealing with some particular topic	preaching the gospel of Christ in the manner of the early church
extended verbal expression in speech or writing
an address of a religious nature (usually delivered during a church service)

discourse (verb)	kerygma (verb)
talk at length and formally about a topic
carry on a conversation
to consider or examine in speech or writing