tough luck vs fate

tough luck and fate both are nouns.

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

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

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

Other hypernyms of tough luck include circumstances, destiny, fortune, lot, luck, portion.

tough luck (noun)	fate (noun)
an unfortunate state resulting from unfavorable outcomes	an event (or a course of events) that will inevitably happen in the future
	the ultimate agency regarded as predetermining the course of events
	your overall circumstances or condition in life (including everything that happens to you)

tough luck (verb)	fate (verb)
	decree or designate beforehand