discourse vs homily

discourse and homily both are nouns.

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

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

discourse: an address of a religious nature (usually delivered during a church service)
homily: a sermon on a moral or religious topic

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

discourse (noun)	homily (noun)
an extended communication (often interactive) dealing with some particular topic	a sermon on a moral or religious topic
extended verbal expression in speech or writing
an address of a religious nature (usually delivered during a church service)

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