First, what the scripture tells us the scripture tells us. However, the desert Mary flew to is prepared for her by God, and Satan cannot reach her other than by rivers of Protestant slander. So, yes, apparently, a different desert.
Thank you though for reminding me that “woman” in “the prophecies” can just as easily be Babylon.
Woman can be many things, but "The Woman" can only be Israel, beginning in Genesis 3 and onward.