calamity vs bad luck

calamity and bad luck both are nouns.

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

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

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

Other hypernyms of calamity include misfortune.

calamity (noun)	bad luck (noun)
an event resulting in great loss and misfortune	unnecessary and unforeseen trouble resulting from an unfortunate event
	an unpredictable outcome that is unfortunate
	an unfortunate state resulting from unfavorable outcomes