Day of rest and Day of the week

Day of rest noun - A day set aside for rest.

Day of the week and day of rest are semantically related. In some cases you can use "Day of the week" instead a noun phrase "Day of rest".

Day of the week noun - Any one of the seven days in a week.

Day of rest and day of the week are semantically related. Sometimes you can replace phrase "Day of rest" with "Day of the week", this phrases are similar.