I know that Jews are forbidden to marry non Jews. This leads me to believe that there is some intrinsic and apparently incompatible difference them. Regardless of this prohibition though, I wonder if, according to the Torah, there is a difference, and what it is.
Yes, there is a big difference between us, and that difference is one of responsibility. Whereas non-Jews have seven rules to keep, the Jewish people were given the entire Torah and all its details to follow. All human beings on this earth were made in the likeness of G-d (Genesis 5:1-2), and are therefore one of G-d's children, but Israel has been likened to G-d's "firstborn son" (Exodus 4:22). Being the firstborn gives us many privileges, but also a lot more accountability and responsibility.
Non jews have the covenant between Noah and God while jews have the covenant between Abraham, Isaac, Jacob and God.
Non jews have less commandments.
Non jews are considered children of God while jews are considered firstborn children of God.
Non jews have a different soul in comparison to jews.
Non jews are not allowed to keep shabbat.
TAKEN FROM CHABAD.ORG: The reason for this prohibition is clearly spelled out in the following verse: "Because he will lead your son astray from Me and they will serve strange gods…" ("Strange gods" can also be interpreted to mean those ideals and ‘isms’ that do not conform to the dictates of the Torah, and before which one bows his head and dedicates his heart and soul.)
The Talmud (Yevamot 23a) points out - and Rashi quotes it in his commentary on the aforementioned verse - that from the precise expression of the verse (he -and not she- will lead your son astray) we can derive two things. In the event that your daughter marries "their son," he will eventually lead astray your sons (in other words, your grandchildren, who will still be considered your sons) from the path of the Torah. In the event that your son will marry their daughter, her children are no longer considered your children, but her children. They are not considered Jewish.
This is a very sensitive question, as the interpretations of that differences might easily become judgemental. I will explain on a very basic level, practically only outlining the framework, without going into details.
A couple of general clarifications first.
- Legally speaking, marrying a gentile does not count in Judaism, but heaving consensual intimate relations with gentiles is prohibited for many reasons (not discussed here).
- In Judaism for something to be forbidden a basic compatibility must be met, i.g. a misdeed must be possible to perform at all, e.g. eating pork is a transgression whereas eating stones is not, illicit relations with gentiles or animals are prohibited whereas intimate relations with plants are not.
Now, to the differences:
In Judaism, every creature is a mixture of material (חומר) and spiritual (רוח). We can also say, for example, that an inanimate object is less spiritual (possesses less spirit) than a plant and even lesser than an animal and even lesser than a human etc. (It can not be expressed in simple percentage though).
To be able to deal with the Torah and fulfill its commandments, the Jews possess a greater degree of (let's call it) "spirituality" than the Gentiles. This is expressed as "Neshamah" and that's the only essential difference. (All other differences stem from this distinction).
Unlike the other aforementioned differences in nature, gentiles are always given an option to compensate that innate "lack" through a conversion to Judaism.
Hope it helps.