fate vs ill luck

fate and ill luck both are nouns.

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

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

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

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

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