Answer: No and No again.
For the people who can read the plain biblical texts know full well that Keturah is an entirely different person than Hagar. However, for those that twist things around because they cannot deal with the fact that the Torah and the Tanach are full of contradictions, they have to do theological acrobatics in order for things to sit well in their unstable mind, the answer to this question above would be "yes."
So let’s delve into the bible and “let’s get biblical” shall we!!
It is in Genesis 25 and in 1st Chronicles 1 that we find the only references to Keturah.
In Genesis 23 & 25, the bible plainly and clearly tells us that after Sarah died Abraham met a lady named Keturah and married her. It also tells us that she gave birth to a total of 6 children by Abraham before he eventually died at the age of 175 years old.
Some people, however, go against what the plain text says and assume that Abraham turned around and married Hagar now as a free woman after the death of Sarah. Thus, erroneously assuming Keturah is Hagar, despite the fact the bible says otherwise.
Why is there so much confusion in the minds of some? Well, one of the main reasons is because they cannot deal with the fact that there is a contradiction in the bible concerning what status Keturah is in. What is that contradiction? Well according to Genesis 25, she is clearly a free woman, she is not a slave to anyone as Hagar was to Sarah. Yet, in 1 Chronicles, she is called a “concubine.”
For those of you that do not know the difference between a wife and a concubine it is this: A “wife” in biblical law is a free woman. A concubine, on the other hand, is a slave girl that belongs to the free woman and the free woman can allow her to get married to her husband. You often see them as “midwives,” or “maidens,” before they become concubines, which accompany a “free” girl that is about to get married or has been married off. At first, these slave girls are usually the slaves of the free girl’s father and he gives them to his daughter as a gift for help and for monetary value.
1st Chronicles chapter 1 makes the mistake of calling Keturah a concubine, and not a wife as Genesis does. This tells us that two different traditions swirled around Keturah. However, to make the erroneous assumption of saying Keturah is Hagar herself is utterly foolish.
Why? This is because it can be confirmed over and over again that she is not. First and foremost, the authors of Genesis and Chronicles make the clear distinction that they are different. Secondly, to confirm this even further the two authors point out that their children are totally different. Let’s look…
In Genesis 17 this is what HaShem says to Abraham…
“And as for Ishmael, I have heard thee: Behold, I have blessed him, and will make him fruitful, and will multiply him exceedingly; twelve princes shall he beget, and I will make him a great nation.”
Then if we turn to Genesis 25 we can find out who those 12 princes are, let’s look:
Now these [are] the generations of Ishmael, Abraham's son, whom Hagar the Egyptian, Sarah's handmaid, bare unto Abraham: And these [are] the names of the sons of Ishmael, by their names, according to their generations:
1 the firstborn of Ishmael, Nebajoth;
2. and Kedar,
3. and Adbeel,
4. and Mibsam,
5. And Mishma,
6. and Dumah,
7. and Massa,
9. and Tema,
12. and Kedemah:
… These [are] the sons of Ishmael, and these [are] their names, by their towns, and by their castles; twelve princes according to their nations.”
Now, if you read a tad bit further you can see where the children of Ishmael lived…
“And they dwelt from Havilah unto Shur, that [is] before Egypt, as thou goest toward Assyria.”
Now, if you read in Genesis 25 or 1 Chronicles 1, you can see that Keturah had six children, whereas Hagar only had one known child, Ishmael.
Here are the children of Keturah and her grand children and great grand children, all found in Gen 25:2-4
As we can see, Keturah is not Hagar, so don’t let anyone fool you to think otherwise, even if your rabbi should tell you this lie. For the source of our information only comes from Genesis and 1st Chronicles, there are no other sources that are relevant. No rabbinical writing is relevant because they wrote their comments hundreds of years after the modern Torah was penned down.