matter vs problem

matter and problem both are nouns.

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

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

Other hypernyms of matter include trouble.

matter (noun)	problem (noun)
that which has mass and occupies space	a source of difficulty
(used with negation) having consequence	a question raised for consideration or solution
some situation or event that is thought about	a state of difficulty that needs to be resolved
a vaguely specified concern
a problem
written works (especially in books or magazines)

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