For instance the God of the Bible is a personal God that cares about humanity. This is not the case in Islam. Obviously a different god.
It's impossible to come to the conclusion that Muslims worship a different god if one reads the Qur'an and/or talks to Muslims about their faith and what they believe.
Below is what Muslims believe:
“We believe in God; and in what was revealed to us; and in what was revealed to Abraham, and Ishmael, and Isaac, and Jacob, and the Patriarchs; and in what was given to Moses and Jesus; and in what was given to the prophets—from their Lord. We make no distinction between any of them, and to Him we surrender.” (Qur'an 2:136)
"...there is no god but He, the Living, the Eternal. He sent down to you the Book with the Truth, confirming what came before it; and He sent down the Torah and the Gospel." (Qur'an 3:2-3)
And here's another verse from the Qur'an:
"So if you are in doubt about that which We have revealed to you, then ask those (The Jews and Christians)
who have been reading the Scripture (The Torah and the Injeel/Gospel)
before you. The truth has certainly come to you from your Lord, so never be among the doubters". (Qur'an 10:94)
Islam is a progressive religion and in the view of Muslims simply a continuation of Judaism and Christianity. If you ever have the opportunity to listen to an Islamic sermon or witness to Muslims you will find that they not only teach and learn from what Muhammad said, but also Moses, David, Jesus, etc.. Islam recognizes the same prophets as Christians.
In this verse the Torah is referred to in the Qur'an:
All food was permissible to the Children of Israel, except what Israel forbade for himself before the Torah was revealed. Say, “Bring the Torah, and read it, if you are truthful.” Whoever forges lies about God after that—these are the unjust. Say, “God has spoken the truth, so follow the religion of Abraham... (Qur'an 3:93-95)
In the following verse the Torah and the Gospel are mentioned and how Jesus fulfilled what is written in the Torah:
In their footsteps, We sent Jesus son of Mary, fulfilling the Torah that preceded him; and We gave him the Gospel, wherein is guidance and light, and confirming the Torah that preceded him, and guidance and counsel for the righteous. So let the people of the Gospel rule according to what God revealed in it. Those who do not rule according to what God revealed are the sinners. (Qur'an 5:46-47)
Once again, Muslims believe in the God of Abraham:
"We will worship thy God, the God of our forefathers Abraham and Ishmael and Isaac, the One God; and unto Him will we surrender ourselves." (Qur'an 2:133)
As you can see from the above verses, there can be no doubt that Muslims are worshiping the same God as Christians and Jews. The Qur'an even tells Muslims to follow the religion of Abraham, and as we we know, Abraham worshiped the one true God.
Here is what Islam teaches about Jesus:
His mother, Mary, was a virgin; Jesus was the "Word" of God; Jesus was the Messiah sent to the children of Israel; Jesus confirmed the validity of the Torah; Jesus lived a righteous life; Jesus performed miracles. Healed the blind, the sick, and raised the dead; Jesus removed some of the law of Moses; Jesus was raised into heaven currently sits with God, and will return at the day of the Resurrection (Judgement Day); and Jesus is the only living profit in Islam
Muslims of course miss the most important aspect of Jesus. That He is the Way, the Truth, and the Life; and the importance of Him being crucified and resurrected as a sacrifice for our sins, but they do acknowledge Jesus and respect Him and His teachings.
Since Muslims do not know Jesus, if you ever plan to witness to a Muslim and you start out by trying to convince them that they are not worshiping the same God, you will push them even further away from Christ than they already are.