"the 10", are part of those 613.
Yes, those... they are part of those 613 of which you just said that they only apply to the people of Israel.
How do you differentiate the "universal" ones from the "specific ones"?
Yes, the 10 are part of the 613, and were also given to Israel. That's why, for example, Gentiles are not required to observe the Shabbat. The Shabbat is a commemoration of our delivery from Slavery. Gentiles, of course, were never slaves in Egypt.
Think of two circles, a smaller circle inside a larger circle. The larger circle is the Law given to Israel at Sinai. The smaller circle is all of the universal laws that are binding on humanity. As you can see, because Jews are people we also have the universal laws within Torah law. Thus part of our Law is "don't murder, don't kill," etc. And part of our Law is just for us, i.e. "keep the Shabbat."
How do you know which laws are universal? Christians usually know because the Jews of the early church wanted Gentile believers to be righteous gentiles rather than converts to Judaism (Acts 15). The Apostles taught these universal laws to their Gentile converts. So basically if you read the Christian scriptures, you will learn the universal laws.
Jews call these laws the Noahide laws, because they were the laws obeyed by Adam and Noah. We have divided these laws into "seven laws" which are actually seven groups of laws. There are Gentiles who have no other religion than believing what Jews believe and following these seven laws. They are variously called Noahides, righteous Gentiles, or God fearers. We have a Noahide here in the forum named Rival -- you should look for him. Here are the seven (groups of) laws:
- Do establish laws.
- Don’t curse God.
- Do not practice idolatry.
- Do not engage in illicit sexuality.
- Do not murder.
- Do not steal.
- Do not eat flesh from a living animal.
By groups of laws, we mean that each law is a starting point for an entire bundle of related laws. For example, take "don't murder." This at it's heart is really don't be involved in illicit bloodshed, even if it doesn't end in death. From there we understand that it bans assault even if it doesn't shed blood. I'm sure you are getting the picture of how it works. Noahides spend time studying these groups of laws.