Question:

If there are 613 commandments, why were ten commandments specifically given at Sinai, and in what way are they different from the other 603?

Response:

To understand this, we first need to clear up a very common misconception. Although in English (and for clarity’s sake, here as well) they are commonly referred to as the “Ten Commandments,” in Hebrew they are called the Aseret Hadibrot, the “Ten Statements.” Thus, the less common English name "Decalogue," derived from the Greek words meaning “ten sayings,” is more accurate.

This isn’t mere semantics.

At Mount Sinai, contrary to common misconception, the Jews received the entire Torah, including all of its 613 mitzvahs, not just the Ten Commandments. The Midrash1 and classic commentators of the Torah explain how each of the Ten Commandments is really a general mitzvah, and they describe how each of the 613 mitzvahs is included in one of the ten statements.2

Furthermore, as the Midrash points out, there are 620 letters that make up the Aseret Hadibrot. This corresponds to the 613 mitzvahs plus the seven days of creation,3 seven Noahide Laws4 or the seven rabbinic mitzvahs.5

Even on a more basic level, the Ten Commandments contain more than just ten specific mitzvahs. For example, according to Maimonidies, the second statement actually contains four separate mitzvahs: (1) not to believe in any other god; (2) not to make graven images; (3) not to bow down to idols; and (4) not to worship an idol in the way it is customarily worshiped.

Yet the Torah itself in a number of places explicitly calls them the “Ten Statements.”6 So what is the significance of specifically ten statements?

The Covenant of Ten

When referring to the Ten Commandments, the Torah calls them the words of the covenant: “...and He inscribed upon the Tablets the words of the covenant, the Ten Commandments.”7 In turn, the Tablets are called Shnei Luchot Habrit, “the Two Tablets of the Covenant.” Thus these Ten Commandments are meant as a covenant between G‑d and the Jewish people.

The Midrash explains that the Ten Commandments correspond to the Ten Utterances with which G‑d created the world (e.g., “Let there be light”), as well as the ten sefirot(Divine attributes or emanations), which are also the source of the corresponding ten faculties (kochot) of the soul.8

Additionally, the Midrash9 explains that the Ten Commandments are connected to the many other things in the Torah that are associated with the number ten: the ten generations from Adam to Noah, the ten generations from Noah’s son Shem to Abraham, the ten tests with which G‑d tested Abraham, the ten blessings our forefathers received, the ten plagues, the ten curtains of the Tabernacle, etc.

The number ten represents wholeness and completeness; thus, all of these ideas are interconnected, reflecting a common purpose.

Purpose of Creation

The Zohar states that “G‑d looked into the Torah and created the world.10” In other words, the Torah is the blueprint for creation.11

The mystics explain that the purpose for creation was that G‑d desired that we make a dwelling place for Him down here in this mundane, materialistic and physical world.12

Thus, our purpose is to refine ourselves and the world around us by using the physical world to serve G‑d, thereby uplifting the mundane and transforming it into something holy.

This is why the number ten is associated with the Torah as well as the creation of the world and the ten sefirot. Through the fulfillment of the Torah and its mitzvahs, we reach the completion of the purpose of creation.13

https://www.chabad.org/library...ndments-at-Sinai.htm