Do Christians and Muslims Worship the Same God?

Second Vatican Council, Nostra Aetate 3, October 28, 1965:
““The Church has also a high regard for the Muslims. They worship God, who is one, living and subsistent, merciful and almighty, the Creator of heaven and earth (Cf. St. Gregory VII, Letter III, 21 to Anazir [Al-Nasir], King of Mauretania PL, 148.451A.), who has spoken to men. They strive to submit themselves without reserve to the hidden decrees of God, just as Abraham submitted himself to God’s plan, to whose faith Muslims eagerly link their own. Although not acknowledging him as God, they venerate Jesus as a prophet, his Virgin Mother they also honor, and even at times devoutly invoke. Further, they await the day of judgment and the reward of God following the resurrection of the dead. For this reason they highly esteem an upright life and worship God, especially by way of prayer, alms-deeds and fasting….
“Therefore, the Church reproves, as foreign to the mind of Christ, any discrimination against people or any harassment of them on the basis of their race, color, condition in life or religion.”