luck vs bad luck

luck and bad luck both are nouns.

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

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

luck: an unknown and unpredictable phenomenon that causes an event to result one way rather than another
bad luck: an unpredictable outcome that is unfortunate

Other hyponyms of luck include mischance, mishap, even chance, toss-up, tossup.

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

luck: your overall circumstances or condition in life (including everything that happens to you)
bad luck: an unfortunate state resulting from unfavorable outcomes

luck (noun)	bad luck (noun)
an unknown and unpredictable phenomenon that causes an event to result one way rather than another	unnecessary and unforeseen trouble resulting from an unfortunate event
an unknown and unpredictable phenomenon that leads to a favorable outcome	an unpredictable outcome that is unfortunate
your overall circumstances or condition in life (including everything that happens to you)	an unfortunate state resulting from unfavorable outcomes