Can anyone tell me if these two entities are related?.
They are the same entity, as is the Jewish god.
Supposedly, all the same. The Muslims think so anyway, calling all the “people of the Book” the “Book” being most of the OT.
However, the devil is in the details. 
Exodus 3:6: Moreover He said, “I am the God of your father — the God of Abraham, the God of Isaac, and the God of Jacob.” And Moses hid his face, for he was afraid to look upon God.
Bob Dylan: God said to Abraham, “Kill me a son” / Abe said, “Man, you must be puttin’ me on”…
This “Abrahamic God” is the same God worshipped by all the so-called Abrahamic religions, of which Judaism, Christianity and Islam are the main three.
Additionally, the Arabs doctrinally trace themselves to Noah’s son Shem, and Muhammad the Prophet of Islam is traced to Abraham’s son Ishmael by Hagar (who were cast into the desert by a jealous Sarah, but saved by God’s providence in the form of a well).
Among Christians, I think only Jack-Chick-caliber loonies don’t think that Muslims and Christians worship the same God. I don’t know of any Jewish groups that claim that the God worshipped by Muslims and Christians isn’t the same one we worship. Each group thinks the other two are wrong about the nature of God, but we think it is the same God.
Really, Christian theology is more disimilar to Judaism than Islam is.
The Jews, Christians, Muslims and Mormons each worship the God of the Old Testament. That they’ve each added their own chapters to the story doesn’t suddenly transmute god into a new “god” just because there’s disagreement about the legitimacy of one or more of the texts. If you think that way you might as well say that Christians, Jews and Mormons all worship different gods. And for that matter why not say that Catholics and Protestants worship different Gods, since obviously there are lots of “details” of theology that are different. But there’s no basis for partitioning off Muslims specifically.
“matter why not say that Catholics and Protestants worship different Gods”
They do. The pope gives credit to saints intervening on his behalf, a supernatural demi-god that other Christians reject.
The “mono” in monotheism is loosely interpreted. There are more independent ghosts, spirits, rankings of angels and saints than the Greeks had.
This is a distortion of Catholic theology. Catholics do not worship saints.
There are angels and demons in Protestant theology as well. Nonetheless, Protestants and Christians still worship the exact same (triune) God.
No way dude! Jack Chick told me Muslims worship the MOON! :eek:
Just kidding! 
AFAIK Islamic and Jewish sages agree on the nature of G-d “He is one and eternally, indivisibly one. He has no human body. He can have no human son.” We just disagree on the status of some prophets and which covenant is the latest and best.
The idea of a trinity (even if the three are also one) makes Christianity the odd man out.
This makes no sense according to Catholic theology. Perhaps “interceding” is the word that you’re after, rather than “intervening”.
Just FYI: Mormons are Christians. Other than that, I liked the rest of your post.
To expand slightly upon this: Catholics ask saints to pray to God on their behalf. I’m not exactly sure how the theology works here, but it makes sense that having somebody in Heaven asking God for you would be helpful.
Some Orthodox Jews have followed Maimonides in classifying Islam and Judaism as safely monotheistic, in contrast to Christianity, which is considered idolatrous due to the influence of Trinitarianism.
However whether that can be considered the same as not following the same God is a different question.
- Tamerlane
In other words, most Muslims and Jews agree that they worship the same God. Most Christians say that they also worship the same God as the Muslims and Jews, but some Muslims and Jews disagree on that.
For the record (and I suspect I’m not telling Monty anything new here) a large proportion of (non-Mormon) Christians regard Mormon belief as outside Christianity owing to some unusual variations in basic theology – which we need not go into, and I presume Monty and other Mormon Dopers won’t object to my inserting that caveat for informational purposes. Obviously, Mormons are strong on the idea that they are as much Christians as anyone else, and in some respects, given Joseph Smith’s description of his prophetic task, perhaps more so than others in their view.
However, I read uglybeech’s post as making reference to variations in Books containing new revelation --the Tanakh, the added material in the Christian Bible, the Qu’ran, and the Book of Mormon/D&C/PoGP, as the basis for his making that fourfold distinction.
What is it that quarterbacks say when they’re about to throw an 80-yard pass in the last 4 seconds when they’re down by 3? 
Uh, they quote the Archangel Gabriel (Luke 1:28)??
Catholics have been at some pains to explain the distinction between seeking intercession through the prayers of another created being – human saint, Virgin Mary, angel, or whatnot – and the worship of God. A blithe soundbite witticism does nothing to refute Diogenes’s comment.
Allah, vs. Jehovah, Father-Son-&-Holy Spirit?
Two distinct and different Powers.
Matthew 7:20 Wherefore by their fruits ye shall know them.