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?
Yes there are many differences.
- Jews are allowed to eat pieces taken from the animal immediately after shechita is performed, even while the animal is still moving
מפרכס (blood must still be removed -- which is harder to do compared
to regular meat, because it was taken alive-ish). Shechita kills the
animal, even if it is still convulsing. (Simla Chadasha
Before digging in, one should wait until the animal stops moving, which is possibly a biblical prohibition of לא תאכלו על הדם (literally, "do not eat on the blood").
- However, a Noahide has to wait until the animal stops moving in
order to be allowed to eat it (27:2).
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.
Therefore, based on the principle "ליכא מידי דלישראל מותר ולעכו"ם אסור" ("there is nothing that is permitted to Jews but forbidden to non-Jews") the convulsing animal would be permitted to Noahides if it's a kosher animal that had a good shechita (i.e. not neveila) and was killed by a Jew, even though it would be forbidden if a non-Jew killed it. (ibid., Shach 27:2)
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]).
These eggs may not be sold to גויים by Jews due to לפני עור, but since eggs are common מצוי it's fine. All the same, they should not be gifted freely, unless there is room to say that they will be used for a non-food purpose, such as for glue or to be incubated/raised by his chickens. If it is clearly for food, such as if it is already cooked, then it is אסור. If there is a food that was cooked with eggs, it is still אסור, because גויים do not have ביטול, even in 1,000 (see this question, which leaves it unresolved whether or not ביטול may be used for גויים, the Chasam Sofer assumes that it may not), and even if it is a נותן טעם לפגם.
[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! :)