Sabbath vs rest day

Sabbath and rest day both are nouns.

Word	Noun	Adjective	Verb	Adverb
Sabbath	Yes	No	No	No
rest day	Yes	No	No	No

As nouns, rest day is a hypernym of Sabbath; that is, rest day is a word with a broader meaning than Sabbath:

Sabbath: a day of rest and worship: Sunday for most Christians; Saturday for the Jews and a few Christians; Friday for Muslims
rest day: a day set aside for rest

Other hypernyms of Sabbath include day of rest.

Sabbath (noun)	rest day (noun)
a day of rest and worship: Sunday for most Christians; Saturday for the Jews and a few Christians; Friday for Muslims	a day set aside for rest