The Mekhilta DeRabbi Yishmael turns to the phrase "and your sojourner in your gates" from the Shabbat (the Sabbath) commandment and asks: which type of sojourner is meant? Jewish law recognizes two distinct categories, and the distinction matters for determining who is obligated in what.
A ger tzedek (a "righteous sojourner") is a person who has fully converted to Judaism, accepting all the commandments and joining the covenant. A ger toshav (a "resident sojourner") is a non-Jew who lives among Israel, does not worship idols, and observes the seven Noahide laws but has not converted.
The Mekhilta argues that "your sojourner in your gates" refers specifically to the ger tzedek, the full convert. The reasoning follows the same pattern used for servants: another verse already covers the other category. (Exodus 23:12) mentions "the sojourner" in the context of Shabbat rest, and that verse refers to the ger toshav, the resident alien.
Since the ger toshav already has his own provision for Shabbat rest elsewhere in the Torah, the reference to "your sojourner" in the Ten Commandments must be addressing someone different. That someone is the ger tzedek, the convert who has fully entered the covenant and is obligated in all the commandments just like a native-born Israelite.
The result is a comprehensive system: native-born Israelites, converts, resident aliens, circumcised servants, and uncircumcised servants all receive Shabbat rest. The Torah simply assigns each group its rest under a different legal provision, ensuring universal coverage through precise legal language.