disaster vs bad luck

disaster and bad luck both are nouns.

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

As nouns, bad luck is a hypernym of disaster; that is, bad luck is a word with a broader meaning than disaster:

disaster: an event resulting in great loss and misfortune
bad luck: unnecessary and unforeseen trouble resulting from an unfortunate event

Other hypernyms of disaster include misfortune.

disaster (noun)	bad luck (noun)
an act that has disastrous consequences	unnecessary and unforeseen trouble resulting from an unfortunate event
an event resulting in great loss and misfortune	an unpredictable outcome that is unfortunate
a state of extreme (usually irremediable) ruin and misfortune	an unfortunate state resulting from unfavorable outcomes