bad luck vs ill luck

bad luck and ill luck both are nouns.

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

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

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

Other synonyms of bad luck include misfortune, tough luck.

bad luck (noun)	ill 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