A fast as to its foundation it involves not eating the manna. The food that represents “what is it” the meaning of the word mana , as something foreign to us as the word of God that works in us.
The Sabbath, a day set aside that we do not have to work to supply us with food necessary for the bodies like bread made from wheat. it is designed as a day to go out with the gospel according to the true fast revealed in Isaiah 58.that loosens the bond of sin, by grace .
It is not just a day for humbling one’s own soul by not eating something. It is the kind of fast that the disciples knew not of and therefore could not cast out the lying demons. But rather a day set aside for setting those captive free from doing the will of the father of lies. As we offer the gospel as our bread it can work in the heart of other as the fruit of God’s Spirit.
The apostate Jews though an oral tradition of men would change the requirement and made it into a self righteous work they could do , even going as far in pride saying they fast twice on the Sabbath . Seeing by that time eating three times was the magic number that they accredited to their own self, as a sign and wonder..as if it was after Christ.
The word week coming from the word sabbaton (singular)is clearly misinterpreted for some reason or other. It was a comparison with the other non self righteous person.
Luk 18:12 I fast twice in the week(on the sabbbath) , I give tithes of all that I possess.
Luk 18:13 And the publican, standing afar off, would not lift up so much as his eyes unto heaven, but smote upon his breast, saying, God be merciful to me a sinner.
The first day of the week is called the Sabbath, not the week made up of the days.I don’t think they have a word for week they would call it seven days. The only time you will find the English word week is in respect to the wrong paraphrase.