The Ten Commandments
With the Seven, we discover what the Bible really teaches. The Seven make up part - an infinitely large part - of the whole Biblical system. Through the Seven, we get the truth about the Bible. This includes the truth that the people of Israel, one of the branches of the Noahide family, constitute a unique nation, and that Israel has a special role to play among her brother Noahides.
As for the Ten Commandments, it outlines the Way of God as it applies to the Children of Israel. The whole Torah or Law of the Bible - all its 613 laws, as Israel has counted them - doesn't apply to everyone.
If one simply looks, one sees that the Ten include Israel's Ten Commandments' obligation to keep the Sabbath at the end of every week. That's not one of the Seven.
Keeping the Sabbath is not one of the basic requisites of civilization. It's a commandment that directly applies only to the Children of Israel. The people of Israel have certain special rules, to help keep God's cause alive in every generation. They constitute a nation only by virtue of the Torah: without the Torah they disappear as a nation. But the world needs its Jewish people. It can't become what God wants it to become without Israel. They help their brother Noahides realize their potential. The Jewish people are a necessary ingredient in the human mix.
The Ten Commandments represent the whole Torah - the Revealed Way or Teaching - of God as it applies to the people of Israel. That includes 613 separate commandments, laws, ordinances, statutes, principles, and symbolic observances. The Ten represents Israel's unique national Way, Israel's religion - in a word, Judaism, in outline.
The Seven represents the whole Torah as it applies to everyone. The Seven represents the Universal Torah: all the Bible's moral (as opposed to ritual) laws and principles. Like the Seven, it serves as an outline to a much larger body of wisdom, at least 60 or 70 principles, within the Torah. The Seven also introduce a whole Way of life.
It's the Seven, not the Ten, that's universal. The Seven represents every Teaching of the Torah which is purely logical. Once one enters the world of moral sanity represented by the Seven and the Torah, every detail of the Seven makes sense logically.