holiday vs half-term

holiday and half-term both are nouns.

Word	Noun	Adjective	Verb	Adverb
holiday	Yes	No	Yes	No
half-term	Yes	No	No	No

As nouns, half-term is a hyponym of holiday; that is, half-term is a word with a more specific, narrower meaning than holiday:

Other hyponyms of holiday include vac, vacay, field day, outing, picnic, honeymoon, paid vacation, winter break.

holiday (noun)	half-term (noun)
leisure time away from work devoted to rest or pleasure	a short vacation about halfway through a school term
a day on which work is suspended by law or custom

holiday (verb)	half-term (verb)
spend or take a vacation