Details of commandment for Gentiles not to eat meat removed from a live animal

[Director Michael]

The commandment not to eat Eiver Min HaChai (meat of a living animal) falls upon animals that have a "distinction between their blood and flesh." Is this distinction based on an animal's anatomy having a closed versus open circulatory system?

No

Or is this based on the Torah's classification of what animals have a distinction between their blood and flesh? If so could you direct me to that source?

Yes. Here is the explanation of that classification in regard to the commandment. The explanation is based on the Torah law.

The verse Genesis 9:4 serves as a prohibition to both Gentiles and Jews against eating eiver min ha'chai: "But the flesh with its soul, its blood, you shall not eat." This establishes that the way it is defined for Gentiles, as to which kinds of creatures the verse is referring, will be clarified by how it is explained in more depth farther on in the Torah, when it is giving more details in the context of the prohibition for Jews.

But it will not be exactly the same, because Jews have some additional dietary prohibitions that don't apply for Gentiles.

The verse Genesis 9:4 itself establishes that we are talking about creatures for which the flesh and the blood are to be considered as distinct entities, in the context of the prohibition. But it doesn't explain what that consideration is, so we need to look elsewhere for that.

Since the verse has application to both Jews and Gentiles, we need to ask, for what creatures is there a distinction between their flesh and their blood for Jews?

If a Jew eats any type of land mammal or bird, kosher or non-kosher, he is separately forbidden to eat the the blood. The Jewish prohibition against eating the blood is in Leviticus 7:26, "You shall eat no manner of blood from a [i.e. any] bird or a [i.e. any] beheimah [the word in Hebrew] in all your dwellings." Beheimah is the general term in Hebrew for a land mammal. So the prohibition of eiver min ha'chai in general is for all land mammals and all birds, with just a few exceptions that we will learn from somewhere else.

For all other creatures that are not land mammals or birds, a Jew is forbidden by only one general prohibition to eat any edible part of them, with no  distinction as to what part it is - flesh, blood, or something else - simply because it is not a kosher species. So the prohibition of eiver min ha'chai does not apply those species.

The exception is that there are a couple of land mammals included in the 8 types of non-kosher sheretz creatures listed in Leviticus 11:29-30. For sheretz creatures, the prohibition to Jews against eating them makes no distinction as to what edible part (flesh or blood, etc.) is being eaten. So the prohibition of eiver min ha'chai is also not talking about any of those species.

Therefore, if flesh is removed from a living land mammal or bird, it is forbidden as eiver min ha'achai for Gentiles, unless it also happens to be one of the sheretz creatures.

There are some additional considerations for Jews as to whether the removed flesh will be forbidden and punishable for them on account of eiver min ha'achai, or on account of some other overriding Jewish dietary prohibition. But that is not relevant for Gentiles, because they have only one dietary commandment, which is not to eat eiver min ha'achai.