ill luck vs hard cheese

ill luck and hard cheese both are nouns.

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

As nouns, hard cheese is a hyponym of ill luck; that is, hard cheese is a word with a more specific, narrower meaning than ill luck:

Other hyponyms of ill luck include weakness, adversity, hard knocks, hardship, gutter, sewer, toilet.

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