I understand that Muslims believe that Allah is God but how can that be?
The word Allah is the Arabic equivalent to the English word God. In addition to its use by Arabic-speaking Muslims, it is also used by Arabic-speaking Christians and Jews. Although they have an incomplete understanding of the nature and revelation of God, Muslims worship the same God whom Christians and Jews worship.
The Church’s relationship with the Muslims. “The plan of salvation also includes those who acknowledge the Creator, in the first place amongst whom are the Muslims; these profess to hold the faith of Abraham, and together with us they adore the one, merciful God, mankind’s judge on the last day” (CCC 841).