August 1 vs quarter day

August 1 and quarter day both are nouns.

Word	Noun	Adjective	Verb	Adverb
August 1	Yes	No	No	No
quarter day	Yes	No	No	No

As nouns, quarter day is a hypernym of August 1; that is, quarter day is a word with a broader meaning than August 1:

August 1: commemorates Saint Peter's miraculous deliverance from prison; a quarter day in Scotland; a harvest festival in England
quarter day: a Christian holy day; one of four specified days when certain payments are due

August 1 (noun)	quarter day (noun)
commemorates Saint Peter's miraculous deliverance from prison; a quarter day in Scotland; a harvest festival in England	a Christian holy day; one of four specified days when certain payments are due