All Abrahamic religions claim to worship the same deity Abraham worshipped. How they know that is of course a different matter,Muslims in fact claim all the prophets including Abraham,Moses and Jesus as prophets of Islam. and Yes all three claim a deity that existed in the universe or pre universe. Its the revelations by their God/Gods that's different like i said Christianity and Islam are totally incompatible at the core.
Well claim yes however one God is one God. Just as there is only one of me as my family "claims" its only one of me and it turns out to be true, then it is. I tend to think primarily Christians of today seek differences between Islam and the Judeo-Christian traditions (I'm not saying you of course are but typically at least un the U.S).
Because I do speak Arabic/Hebrew I can break it down as far as linguistically (in association to the historical facts that many scholars also argue). When Muslims refer to Allah, there is little phonetical difference when translating it to Hebrew and even Aramaic. Jesus, who historically was a Jew refer to God as Alaha in Aramaic, which is the language spoken by the Jews in that time (as well as Greek). Now because Arabic is apart of the Semitic language how Jews and eventually "Jewish Christians" after Jesus, communicated their faith to the One God in the most common language spoken at the time which was Aramaic.
Since travelling to Jerusalem I actually had the priviledge to speak to some Rabbi's about this matter some time ago and from what I understand Allah or Eloh (Eh-Low) are written the same (when writing Allah in Hebrew script).
Why do all of this matter?
Well, if me and my siblings are going to communicate our needs to our mother (or father) we will address them by the most common name we know, that is most commonly the name "mom" or "dad"-yes it sounds quite retarded but I'll explain. Surely, if we are talking about fundamental differences in addressing the claim of worshipping One God what are the fundamental differences?
For the Christian, Jesus is god. Well, ok but historically that wasn't the case when Jesus existed according to some Biblical scholars. Also, Constantine the ruler of the Byzantine period, had a great influence as to how Jesus' divinity would be addressed which was to combat Arianism. But heck, even Jesus himself made the distinction perfectly when he said:
"Ye have heard how I said unto you, I go away, and come again unto you. If ye loved me, ye would rejoice, because I said, I go unto the Father: for my Father is greater than I"-John 14:28
Now surely, if Jesus was God the Creator and God the human in one body why make such a confusing distinction? I'm sure Christians would come up with a bunch of non-scholarly excuses but that is besides the point.
The fact that Christians hold Jesus to be God incarnate is not a divine epiphany as Paul expressed on the road to Damascus, but rather the result of royal influence. Now, when it comes to Jews, Jews simply reject Jesus as the Messiah and God because
1) Christianity broke away from Jewish tradition when you make God into a human
2) Jesus failed his mission as the messiah since, there are certain criteria as expressed in Jewish theology that will dictate if the messiah is real. One good example I read was there would be peace on Earth when the messiah comes (How many wars has the earth been through since Jesus' departure?)
The "Jewish Christians" according to scholars have mentioned that during Jesus' time they would observe Jewish customs (observed Sabbath etc) and even in the Bible, Jesus in the temple recited the Sh'ma Yisrael (Hear O'israel the Lord our God is One)-which contradicts the trinitarian philosophy. The only break of these traditions we know is when Paul came.
Again fundamental differences weren't the result of any divine influence or metaphysical influence but because of historical figures and in psychology as we psychologist would say the "zeitgeist" changed religious history.
Now, with respect to Islam and Judaism Islam strictly enforces strict monotheism. God is one, indivisible, no partners, no equals, or any partners co-equal. The same principle is mentioned by Jews. Jews and Muslims don't say God cannot come in the form of a human and save the world as expressed by Christians, but they say (from what I read) God's morphing in human form to sacrifice himself for the would runs counter to the abilities God has. For instance, God can create the entire universe with all its complexity and chaos but in order to save puny organic matter aka human beings he needs to change into a human and die on a piece of carved wood.
Jews and Muslims may find Christians mistaken, but me personally looking at the historical aspect-Christians believe in One God (Eloh, Alaha, YHVH, or whatever you call God).
The only significant difference I personally see after my extensive readings is the difference in prophetic figures (Jesus, Muhammad). Jews don't acknowledge Muhammad, but Jews acknowledge that Muslims worship the God of Avraham because one of the philosophies Jews express is that in the Noahide code, believing in One God is one of the laws a gentile has to follow to have a place in the world to come so there is no rejection of Islamic monotheism in Judaism.
For the hard headed Christian, without mentioning Jesus being God or whatever, a Muslim can say there is only one God in this universe-A Christian might reply (yes Jesus) and so on and so forth and they both get into an argument. But at its core without the specifics, if you simply focus on the theological aspect looking at the Sh'ma Yisrael, The Holy Qur'an, and parts of the Bible-All three faiths believe in One Creator. One God is One God, and the only mistakes we can find are the specifics but as I mentioned with respect to Christianity those specifics came way after Jesus died and were not of any divine providence. Sorry this was a long winded post.