hard cheese vs tough luck

hard cheese and tough luck both are nouns.

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

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

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

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