Rather than playing word games, wouldn't it be easier to ask Muslims whether their god is the god of the Judeo-Christian Bible? Isn't that what matters?
I asked an Muslim girl I know this once (she's married to a Catholic so religious discusions between the three of us are always fun). She told me that the god of the old testament is Allah but the bible is inaccurate, and that Jesus is not Allah but instead just one of his prophets.
Interestingly in the course of discussions with her I discovered that almost everything I had been told about Islam by the church I use to attend was false (or when I'm feeling less charitable, a lie).