matter vs consequence

matter and consequence both are nouns.

Word	Noun	Adjective	Verb	Adverb
matter	Yes	No	Yes	No
consequence	Yes	No	No	No

As nouns, consequence is a hypernym of matter; that is, consequence is a word with a broader meaning than matter:

Other hypernyms of matter include import, moment.

matter (noun)	consequence (noun)
that which has mass and occupies space	having important effects or influence
(used with negation) having consequence	the outcome of an event especially as relative to an individual
some situation or event that is thought about	a phenomenon that follows and is caused by some previous phenomenon
a vaguely specified concern
a problem
written works (especially in books or magazines)

matter (verb)	consequence (verb)
have weight; have import, carry weight