day of rest vs day of the week

day of rest and day of the week both are nouns.

Word	Noun	Adjective	Verb	Adverb
day of rest	Yes	No	No	No
day of the week	Yes	No	No	No

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

day of rest (noun)	day of the week (noun)
a day set aside for rest	any one of the seven days in a week