To some degree, morality comes from many directions...culturally, biologically, religiously, economically, environmentally, politically and even circumstantially based to name a few.
Is the question you are asking....whether one trumps the other or do ALL morals come from God or a deity?
The fact that morals differ between groups tell me that there is more to it than religion. That does not, in my mind, eliminate the existence of God. Nor does it mean that my religions is the only basis for my moral choices.
For example, I am a strict vegetarian for ethical reasons, but the clergy and followers of my faith condone meat eating. In that case, one might say my moral choices expand outside the tenets of my faith. On the flip side, over the course of my lifetime, not all the choices I have made might be considered moral.