discord vs disagreement

discord and disagreement both are nouns.

Word	Noun	Adjective	Verb	Adverb
discord	Yes	No	Yes	No
disagreement	Yes	No	No	No

As nouns, disagreement is a hypernym of discord; that is, disagreement is a word with a broader meaning than discord:

discord (noun)	disagreement (noun)
strife resulting from a lack of agreement	a difference between conflicting facts or claims or opinions
a harsh mixture of sounds	the speech act of disagreeing or arguing or disputing
disagreement among those expected to cooperate	a conflict of people's opinions or actions or characters
lack of agreement or harmony

discord (verb)	disagreement (verb)
be different from one another