A Christian is a person that is recognized as a member of one of the many chapters of Club Christian.
A Muslim is a person that i recognized as a member of on of the chapters of Club Islam.
It really is that simple.
As to the Genesis creation myths, the methods used are different, the order of creation is different, the two gods described in the stories are different.
You can claim they are the same but the God in Genesis 1 is aloof, overarching, creates by an act of will alone, acts without hesitation and uncertainty but is also separate from his creation, not interacting.
The God in Genesis 2&3 though is unsure, a hands on tinkerer learning on the job, sometimes afraid, but also very human, interacting directly with the creation.
Two different gods, two different creation myths.
The question is though, why prefer those stories to any of the many others?
Anyone so limited that they can only spell a word one way is severely handicapped!