Lord's Day vs rest day

Lord's Day and rest day both are nouns.

Word	Noun	Adjective	Verb	Adverb
Lord's Day	Yes	No	No	No
rest day	Yes	No	No	No

As nouns, rest day is a hypernym of Lord's Day; that is, rest day is a word with a broader meaning than Lord's Day:

Lord's Day: first day of the week; observed as a day of rest and worship by most Christians
rest day: a day set aside for rest

Other hypernyms of Lord's Day include day of rest.

Lord's Day (noun)	rest day (noun)
first day of the week; observed as a day of rest and worship by most Christians	a day set aside for rest