According to some sources like …
When I have researched the ten commandments and the law of Moses some sites say they are the same, others say they are different.
What is the truth?
Which laws from the Old Testament were abolished by the death of Christ and which were not, if any?
What causes confusion is that the term “the law” can apply to several different things depending on the exact context. There is no single right-or-wrong way to use the term, instead it has different applications and many layers.
In one sense, the phrase “the law” can refer to the first 5 books of the Bible; aka “the Pentateuch” or “the law of Moses” or “the Torah.”
Even broader than that, in a Jewish context it can also include accepted rabbinic applications of the Law of Moses known as the Talmud. The Talmud is then divided into the Mishnah (actual text of the rabbinnic law) and the Gemara (commentary on the law, often written well after the fact).
The 10 commandments (of course) are part of the Torah (the actual biblical text) but they are not seen as the entirety of the Law, instead the most important part of it, or the summary of it.
The way the term is used in the New Testament, “the law” us usually referring to the Talmud; that is, the Law in its broadest sense, including the way it was interpreted and applied, and especially according to the Pharisaic school of thinking.
Back to your question:
Briefly speaking, Christians accept the 10 Commandments as being still binding.
Purity laws (eg Kosher foods) have been abolished.
Ritual laws (eg temple worship) has been replaced by Christian ritual laws.
Social or civic laws (eg those dealing with property boundaries) have been replaced by civil laws but can still be binding in principle, especially if they express natural law (again, property boundaries is a good example)
That’s a start. Understand please that it’s a very brief one.