Other contributors have said "Is a Arabian red fox a variation of the red fox?" is the same question as "Is an Arabian red fox a variation of the red fox?" If you believe that these are not asking the same thing and should be answered differently, click here
Arabian foxes are a subspecies of red foxes and are adapted to desert life more. They have larger ears and smaller bodies as well as fur between their toes - adaptions that the red fox don't have.
No, they aren't. In fact, they're pretty much never "red" (except in the sense that some people have "red" ... actually more orange ... hair). See the related link for some pictures of the pelts of...