I would have to say that a different conception of God amounts to a conception of a different God when certain people, whether out of ignorace or because they have a particular agenda they want to promote, strart making claims to that effect.
It think a lot of it comes down to an “Us vs. Them” mentality. Muslims are perceived as being “Them”, so, because “They” (Musims) have a different concept of God that “Us” (Christians) then it is obviously because “They” worship a different God.