But they still don't keep it the way Jews are supposed to. They just close their stores but still do melacha, which is fine, because they're not supposed to keep it.
As far as I know, Christians are supposed to uphold every one of the Ten Commandments. They're the fundamentals of Christianity. Yes, and you're right that Jews have to keep them, but just as much, plus, keep the other hundred-plus commandments the Torah commands of us.
Christians cannot committ adultery, must honor their neighbor, cannot steal, cannot kill, etc. Those are part of the Ten Commandments.
But the reason they can't do that is because it's in The Noahide Laws. Keeping Shabbat is not in The Noahide Laws. The Ten Commandments is only for Jews. Why don't Christians follow the other 613 mitzvot if they want to keep Shabbat?
The mitzvot is for Jews, as well as the Ten Commandments. Christianity is a derivative of Judaism, but it's a totally different religion, based on their beliefs and what is written in the Christian bible. Christians who break any of the Ten Commandments will be punished. They must uphold the Shabbat, but they observe it on Sunday. They also don't have as many prohibitions to abide.
Who will they be punished by?
By the way, The "Ten" Commandments actually contain 12 mitzvot. In Hebrew The Ten Commandments are called The Ten Sayings. Two of the sayings contain two commandments. I think an example is "Refrain from idol worship." (Positive) and "Don't practice idolatry." (Negative). The Ten Commandments are only a down payment to the rest of The Torah, the rest of which Christians don't follow at all except for occasional things such as not taking interest on loans which they are permitted to by Torah law because they are not Jewish.
Christians who break any of the Ten Commandents will be punished by G-d. Christianity and Judaism are horses of a different color. They share many of the same principles, but on the whole are totally different.
The Commandments have different interpretations between the two faiths, especially due to the mitzvot that Jews have to abide.
Christianity has little to do with the Torah as a whole. Many of the commands in the Christian bible are derived from the Torah, but most of it is totally different from the Torah.
Comparing the two is almost worthless, because they are so different.
Need a strong example of how different they are? How about when it comes down to the identity of The Messiah? Christians already who their Messiah is. Jews do not.
So, yes, there are, indeed, similarities and derivatives, but you really can't put them in the same boat.
Now, if you're talking about the Jewish point of view that's different.