The entire western world borrowed the concept of the week from the Jews (who may or may not have borrowed it from other societies in Mesopotamia), so their tradition is our best authority for determining the numbers that go with each day of the week. Since the days of the Jewish Week have no names apart from their numbers, the numbers are pretty obvious.
The first day of the week starts on Saturday right around sunset, and ends at the same time on Sunday. The Seventh Day (The Sabbath) starts at sundown on Friday and ends at sundown on Saturday.
Sunday is the first day of the week, or the eighth day. It is not the sabbath, or even "the christian sabbath." It is The Lord's Day. There is no reason to make it into a day of rest, unless you just really like following Roman Civil Law passed under Constantine (which arguably may have been in honor of Sol Invictus instead of Christ). The Lord's Day is a day for worship, fellowship, and charity work. In the early church it was the norm for Christians of Jewish descent to keep all the customs of the Jewish Sabbath, and then meet together on The Lord's Day to commemorate the Resurrection. The New Testament does contain the command that the church meet together from time to time, but never sets a specific schedule. Any time would do, but in honor of the resurrection Sunday quickly became traditional.
Muslim's do not keep the Sabbath, or even pretend to do so. They teach that the Sabbath was part of the Covenant made with the Jews at Mount Sinai, and never was incumbent upon gentiles, including the other children of Abraham. (Orthodox Judaism teaches the same thing in that regard.) Much like Christians, they were ordered to meet together from time to time in prayer and fellowship. Friday was given as a time to do this, although the choice was fairly arbitrary. The reasoning there was probably very similar to that in the Didache, which recommends that Christians fast on the 4th and 6th days of the week rather than the 2nd and 5th because that is what "the hypocrites" do. They just chose it because it was close to what other Abrahamic faiths did but still different enough to set them apart as a distinct community. They were never given a day of rest and do not have regulations against working on Friday so long as they take come time off to pray.
Over time, many Christians (falsely) came to see Sunday as their Sabbath, and so refused to work on the 1st day. Because of this very little business was done on that day. Jews continued to take off the 7th day, and where they were a significant minority it was often not profitable for their Christian neighbors to stay open either. When the labor movement started pressing for reduced hours and days in the work week, these were the obvious choices of days for almost everyone to take off so as to get more work out of those religiously motivated to take one of those days off.
