Do muslims and christians worship the same God?

Muslims worship Allah. Alot of muslims and christians will tell you that Allah is just Arabic for God. This is not true. Allah is the name of the god of the quran. Take the islamic affirmation as an example...

La Ilaha ha Ila Allah

Translation: There is no Ilah (God) except Allah

The God of the bible' name is not Allah.

Another thing I have found when studying the quran and the bible is the major difference on the subject of Israel. The quran says that the last day will not come until the muslims confront the jews and destroy them. The bible says that Israel is God's chosen people and God will fight her enemies. How can these two books be inspired by the same God?

God of the bible God of the qur'an
Jesus is the Son God has no son
God is a triune being God is not a trinity
Man can know God personally (John 17:3) Allah is unknowable
God is love (1John 4:16) 99 illustrious names but not one is love or loving
Grants salvation by the gift of grace Gives salvation based on works

The one true God, the God of the bible is a trinity; God the Father, God the Son and God the Holy Spirit. Muslims worship Allah and deny the trinity. Hence Muslims DO NOT worship the same God.
Allah is a false god. Islam is a revival of the pagan moon god cult. See Deu 4:19, 17:3
Can Islam take criticism?