hardship vs difficulty

hardship and difficulty both are nouns.

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

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

hardship: something hard to endure
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 hardship include difficultness.

hardship (noun)	difficulty (noun)
something hard to endure	an effort that is inconvenient
something that causes or entails suffering	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 misfortune or affliction