This is correct. Islam teaches that each prophet was given specific guidance and laws for the people of their time. With Muslims believing that Muhammad was the final prophet, they follow what is found in the Qur'an and Sunnahs to this day.
Below is the closest thing found in Islam to the Ten Commandments.
Say, “Come, let me tell you what your Lord has forbidden you: that you associate nothing with Him; that you honor your parents; that you do not kill your children because of poverty—We provide for you and for them; that you do not come near indecencies, whether outward or inward; and that you do not kill the soul which God has sanctified—except in the course of justice. All this He has enjoined upon you, so that you may understand.”
And do not come near the property of the orphan, except with the best intentions, until he reaches maturity. And give full weight and full measure, equitably. We do not burden any soul beyond its capacity. And when you speak, be fair, even if it concerns a close relative. And fulfill your covenant with God. All this He has enjoined upon you, so that you may take heed. (Qur'an 151:152)
While it doesn't mention the Ten Commandments specifically, the Qur'an does acknowledge that God's law was given to Moses and the children of Israel through the Torah.
We gave Moses the Scripture, and made it a guide for the Children of Israel (Quran 17:2)
We gave Moses the Scripture, perfect for the righteous, and explaining everything clearly, and a beacon, and mercy, that they may believe in the encounter with their Lord. This too is a blessed Scripture that We revealed; so follow it, and be righteous, that you may receive mercy. (Quran 6:154-155)
“O Moses, I have chosen you over all people for My messages and for My Words. So take what I have given you, and be one of the thankful. And We inscribed for him in the Tablets all kinds of enlightenments, and decisive explanation of all things. “Hold fast to them, and exhort your people to adopt the best of them. (Qur'an 7:144-145)
...they have the Torah, in which is God’s Law... Yet they turn away after that. These are not believers. We have revealed the Torah, wherein is guidance and light. The submissive prophets ruled the Jews according to it, so did the rabbis and the scholars, as they were required to protect God’s Book, and were witnesses to it. (Qur'an 5:43-44)