problem vs difficulty

problem and difficulty both are nouns.

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

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

problem: a source of difficulty
difficulty: the quality of being almost beyond one's ability to deal with and requiring a great effort to achieve a positive result

Other hypernyms of problem include difficultness.

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

problem: a state of difficulty that needs to be resolved
difficulty: the quality of being almost beyond one's ability to deal with and requiring a great effort to achieve a positive result

Other hypernyms of problem include difficultness.

problem (noun)	difficulty (noun)
a source of difficulty	an effort that is inconvenient
a question raised for consideration or solution	the quality of being almost beyond one's ability to deal with and requiring a great effort to achieve a positive result
a state of difficulty that needs to be resolved