ill luck vs fate

ill luck and fate both are nouns.

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

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

ill 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 ill luck include circumstances, destiny, fortune, lot, luck, portion.

ill 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)

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