January 1 vs public holiday

January 1 and public holiday both are nouns.

Word	Noun	Adjective	Verb	Adverb
January 1	Yes	No	No	No
public holiday	Yes	No	No	No

As nouns, public holiday is a hypernym of January 1; that is, public holiday is a word with a broader meaning than January 1:

Other hypernyms of January 1 include legal holiday, national holiday.

January 1 (noun)	public holiday (noun)
the first day of the year	authorized by law and limiting work or official business
(Roman Catholic Church) a holy day of obligation
(Roman Catholic Church and Anglican Church) feast day celebrating the circumcision of Jesus; celebrated on January 1st