Are African-Americans and Hebrew Israelites the same people?

Answer 1

If you believe that all races descend from Adam, yes.

Answer 2:

Those called African Americans are Israelites, yes; that is, the blood descendants of the Israelites spoken of in Scripture.

Answer 3:

No, that claim has been thoroughly debunked by actual DNA testing of both groups.

Answer 2

No; that is a fanciful notion, or wishful thinking, contradicted by DNA studies.
Just as today, Israelites came in differing skin-tones, heights, and body-types. Our tradition is that the twelve sons of Jacob (the 12 Tribes) were not completely similar to each other in appearance, though none of them was really dark-skinned (Rashi commentary on Genesis 12:11).

Abraham and Sarah came from southern Iraq and their wider family from northern Iraq. Since DNA tests have shown that Jews intermarried infrequently throughout history, Abraham and the Israelites probably looked like Jews today.

DNA testing of Jewish communities worldwide has shown that they are all interrelated and of Middle Eastern genetics, not African or Egyptian.

In 2000, the analysis of a report by Nicholas Wade "provided genetic witness that Jewish communities have, to a remarkable extent, retained their biological identity separate from their host populations, evidence of relatively little intermarriage or conversion into Judaism over the centuries. The results accord with Jewish history and tradition." (See: What race were the Israelites?)

The only exception to this is the Ethiopian Black Jews, who show only a trace of DNA connection to other Jewish communities. Western ethnologists today hold the view that the Jews of Gondar (Ethiopia) either emerged from a Judaizing strain among Ethiopian Christians, or were converted by Yemeni Jews who crossed the Red Sea.

A study by Professors Lucotte and Smets has shown that the genetic father of Beta Israel (Ethiopian Jews) was close to the Ethiopian non-Jewish populations. This is consistent with the theory that Beta Israel are descendants of ancient inhabitants of Ethiopia, not the Middle East.

Hammer et al. in 2000, and the team of Shen in 2004, arrive at similar conclusions, namely that the DNA of the Ethiopian Jews probably indicates a conversion of local populations.
It has been estimated that this happened some 2,000 years ago.

And in America:
The beliefs and practices of Black Hebrew groups vary considerably. The differences are so great that historian James Tinney has suggested the classification of the organizations into three quite distinct groups.
Some of these groups are actually Christians, or part-Christians in their beliefs and practices. They have titles such as Church of the Living God, the Church of God and Saints of Christ, and the Israelite Church of God in Jesus Christ. Others profess beliefs closer to Judaism, such as the Commandment Keepers.
As Judaism sees it, the issue with their claims is that they can produce no generally-accepted evidence of actual Semitic ancestry. These groups created themselves spontaneously within recent decades, from within the wider African-American population.

Answer 3

The specific term "Hebrew Israelites" is a term used exclusively by the African-American Churches that believe that they are the descendants of the Biblical protagonists. In that case, the question is self-answering.

However, if by the term "Hebrew Israelites", the intended meaning was the "Ancient Israelites", then the answer is NO. There is no scientific evidence that the peoples of Africa are in any way connected to the Ancient Israelite Tribes. If anything, the Lost Tribes of Israel would be assimilated into the Middle East. The Black Israelite Churches believe that this is the case regardless of this evidence. They also believe this in spite of the facts that many of the peoples they consider to be Israelite Tribes are either wholly or partially mixed with non-Blacks (such as Whites or Native-Americans). This should cause major theological problems since the Black Israelites' claim to be the true Israelites rests on the fact that they were moved by ships and sold in distant lands which did not occur for either Whites or Native-Americans.