I think that it’s important to remember the distinction of beliefs about God. Catholics believe in the same God as do the Jews (the God of Abraham, Issac, and Joseph) but the Jews don’t accept Jesus as the messiah. Because of this, we say that we believe in the same God as do the Jews but they don’t agree with that.
The Muslims believe in the God of Abraham according to the teachings of Mohammed. They believe that there is only one God, that He is good, merciful, and will judge us on the last day. These four qualities (one, good, merciful, and judge) are the extent to which we hold common belief with the Muslims and the only sense in which we can say that we believe in the “same” God. This is the sense in which the Church expresses these statements. In respect to the other beliefs that Muslims have about God, we do not believe the same as they do and the Church doesn’t and never intends to teach that we do.