Both Jews and Noahides are forbidden to eat aiver min hachai (a limb torn from a live animal).
Is there any difference between the prohibitions for Jews and non-Jews?
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Yes there are many differences.
This leads to an interesting paradox -- after an animal was killed, while it is still moving, it is permitted to Jews and forbidden to non-Jews.
Rambam (Melachim 9:10) also says that while a Jew is only culpable for a shiur (kezayis) of eiver min hachai, the non-Jew is culpable for any amount of eiver min hachai. (see later in this answer for more from the Rambam on this topic)
Chasam Sofer (Tshuva 19, brought by Pischei Tshuva 62:1) says that since eggs are really eiver min hachai (see this answer), and only became מותר to Jews from a דרשה in a פסוק, since the non-Jews never got the Torah, they never got the allowance to eat eggs. Now, because of ליכא מידי, eggs that Jews are allowed to eat are also permitted to non-Jews [ignoring the רמב"ם, who doesn't hold of ליכא מידי (he writes that even if a Jew killed it, it would still be forbidden to non-Jews), and therefore all would be אסור].
However, this means that those eggs that are not לישראל מותר, would still be forbidden to non-Jews. This includes ביצי טריפה [the eggs of kosher animals that have certain bodily defects such as torn lung, broken leg/wing in certain locations etc.], and ביצי טמאה [non-kosher animals, such as hawks or snakes] (those are his examples, I would add the eggs of a chicken that you hit, that is eiver min hachai [see here again], as well as fertilized eggs [the ones with blood spots]).
[We do not פסקן like the Rambam that does not hold of ליכא מידי due to the Simla Chadasha mentioned above, but all the same, according to Chasam Sofer one would not be allowed to sell ביצי טריפה\טמאה, and one might argue that when he is the only egg vendor (=not מצוי) it would be אסור as well]
Credit for the Rambam, Shach and Chasam Sofer go to Yoni. Thanks! :)