Many denominations refer to Sunday as "the Christian Sabbath." Yet, nowhere in Scripture do we find such a term in reference to a day of the week.
Our English word "sabbath" derives from the Greek, "sabbaton." It means a rest, or cessation from all activity. Were this to apply to a day, believers would have to follow exactly what is written in the old law of Moses to the jot and tittle.
The believer's rule of life is not the Old Testament sabbath. The ten commandments were a code of law given specifically to the nation of Israel (Exodus 20:1ff). The Lord Jesus Christ came and fulfilled it in every jot and tittle. In Hebrews 9:9,10 it shows clearly that the Old Covenant was in force until such time as the Reformation, that is the first coming of Christ, whereby He fulfilled it and set it aside.
Those who enter into this New Covenant relationship with Christ, by His Spirit and Sovereign grace, are instructed to ignore to old way and tradition, Colossians 2:16,17. This is why the apostle Paul taught that God approves believers who esteem every day alike.
The believer's sabbath is not a day, but Christ Himself. Our rest is found in the Lord Jesus Christ as Mediator and the Surety of the "better covenant." This is the meaning of Hebrews 4:9,10.
If you are the Lord's you have ceased from your own dead works, and you live now by the faith of the Son of God, who loved you and gave Himself for you. Christ has fulfilled all the work of God required for the salvation of His people. We rest in Him.
This does not mean that we neglect meeting together with God's people. The early church met the first day of the week (Sunday) in memory of Christ's resurrection. They met often on the other days as well, Acts 2:46. We meet because we love this One who is our Sabbath.