hard cheese vs ill luck

hard cheese and ill luck both are nouns.

Word	Noun	Adjective	Verb	Adverb
hard cheese	Yes	No	No	No
ill luck	Yes	No	No	No

As nouns, ill luck is a hypernym of hard cheese; that is, ill luck is a word with a broader meaning than hard cheese:

Other hypernyms of hard cheese include bad luck, misfortune, tough luck.

hard cheese (noun)	ill luck (noun)
bad luck	an unfortunate state resulting from unfavorable outcomes