problem vs matter

problem and matter both are nouns.

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

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

Other hyponyms of problem include pressure point, can of worms, deep water, growing pains, hydra.

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

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