bad luck vs tough luck

bad luck and tough luck both are nouns.

Word	Noun	Adjective	Verb	Adverb
bad luck	Yes	No	No	No
tough luck	Yes	No	No	No

As nouns, bad luck and tough luck are synonyms defined as:

bad luck and tough luck: an unfortunate state resulting from unfavorable outcomes

Other synonyms of bad luck include ill luck, misfortune.

bad luck (noun)	tough luck (noun)
unnecessary and unforeseen trouble resulting from an unfortunate event	an unfortunate state resulting from unfavorable outcomes
an unpredictable outcome that is unfortunate
an unfortunate state resulting from unfavorable outcomes