Before we attempt to answer your specific question, let’s look at the passage in Isaiah that you are obviously referring to. It is found in Isaiah 58:13-14, “If you turn away your foot from the Sabbath, for DOING YOUR OWN PLEASURE on My holy day, and call the Sabbath a delight, the holy day of the LORD honorable, and shall honor Him, NOT DOING YOUR OWN WAYS, NOR FINDING YOUR OWN PLEASURE, NOR SPEAKING YOUR OWN WORDS, then you shall delight yourself in the LORD; and I will cause you to ride on the high hills of the earth, and feed you with the heritage of Jacob your father. The mouth of the LORD has spoken” (NKJV).
So, the children of Israel were not only to abstain from having any “personal pleasure” on the Sabbath Day, they were also to refrain from “personal gain” by working. This day was to be wholly committed to the Lord, either by worshipping Him or by serving Him by “serving others” by caring for “the oppressed, the hungry, the poor, and the naked” (see verses 6-7 of Isaiah 58).
Believers today, who make up “the church of God,” are NOT under the law of Moses, but under the grace of our Lord Jesus Christ. In John 1:17 and Romans 6:14 we read, “For the law was given through Moses, but grace and truth came by Jesus Christ….you are not under law but under grace.” This means that the law of “observing the Sabbath Day” does not apply to us. Some may not see this and judge us for not “keeping the Sabbath.” The apostle Paul addressed this issue in Colossians 2:16, “So let no one judge you in food or drink, or regarding a festival or a new moon or SABBATHS.” There will be those who say, “Christians don’t have to ‘keep the Sabbath,’ but the Lord’s Day (Sunday) is our day of rest in which we worship the Lord and serve Him by serving others.” They may also go on to say, “On the Lord’s Day we should refrain from all work and personal pleasure.” I do agree that the Lord has, in His sovereignty, given us the “Lord’s Day” so we can come together to worship Him in the breaking of bread and to minister to one another (see Acts 20:7), but it is NOT a day to be OBSERVED IN A LEGAL WAY and it is certainly NOT PUNISHABLE BY DEATH if we don’t follow the restrictions that were given to the Jews.